England are still in this World Cup. Next stop is a Saturday showdown with Sri Lanka in Sydney.
Bye for now.
Post update
So it's eyes down for Friday and Saturday. Before then, attention switches to Group Two, where it looks like a three-way scrap between India, Bangladesh and South Africa.
Post update
More from England captain Jos Buttler: "We've had a lot of success batting first, it's something we want to be brave with and take that option sometimes. It's definitely an aggressive option and it was the right one today.
On Alex Hales: "He played brilliantly. We know what he's capable of, he's taken his chance to get back in the side.
"You have to be patient in T20 cricket, it's easy to critique and write people off after a few low scores but you're asking people to play a high-risk game. You've got to give them that safety net and encourage them to keep taking the game on.
On Adil Rashid: "I feel for him a bit, Adil has been bowling really well without the rewards that he's probably deserved. He had some tough luck with his best mate dropping one off him today but he's going to take plenty of wickets for us going forward, no doubt."
Post update
I'm really sorry to say this, but I can't shake an uneasy feeling about England needing to beat the Chris Silverwood-led Sri Lanka to go through.
Post update
To mark your card, the Ireland-New Zealand and Australia-Afghanistan games are both in Adelaide on Friday.
England play Sri Lanka in Sydney on Saturday knowing exactly what they have to do.
'England bowled better than us'
New Zealand's Glenn Phillips, speaking on Test Match Special: "It's a tough one. When a team gets 179, you're either going to get really close or nowhere near I reckon. We gave it our best shot but they bowled really well and were the better team today.
"I think on a big ground, trying to chasing 16s in the last three overs is tough. We had our plans in mind and tried to take it as deep and as close as possible but the way England stuck to their bowling plans made it tough for us to have any massive overs.
"It's a real credit to how the England boys bowled."
'England impressive from ball one'
Ben Cutting
Former Australia all-rounder on BBC Test Match Special
England were impressive and it started from ball one and the way they took on the powerplay with Alex Hales. We've seen a number of innings on this pitch now and we thought a par total was about 150 or 160, and they went well past that.
That win can provide England with the momentum that they need.
'The guys closed the game out beautifully'
England all-rounder Sam Curran on Sky Sports: "The decision to bat first was something that Jos wanted to do so we could get out there and at them, on a wicket that looked quite tricky.
"There is no panic. We went wrong in the Ireland game, and we knew New Zealand are a good team and I thought with three or four overs to go that I'd be having to defend 10 in the last game but the guys closed the game out beautifully at the end.
"The dimensions are big so we knew if guys are hitting for six they have to play a really good shot. We had our plans but Glenn Phillips got going and made it tough. He is a quality player and his confidence is really high. They are an amazing team and if we go well on Saturday we might have to face them again, you never know."
'Hats off to England, they were clinical'
New Zealand captain Kane Williamson: "Credit to the way England played. They put us under pressure from the get-go with the bat and we struggled to get the breakthroughs to change the momentum. It was a tough surface, but they played beautifully. We were in the game second half and we needed a few things to go our way but hats off to England, they were clinical.
"They were probably above par but it is what it is. We were just trying to take it deep and we had our moments but we weren't able to get ahead of the game. Credit to the way they bowled - it was tricky with the big boundaries.
"Jos is one of the best players in the world so you don't want to drop him twice and he'll probably make you play. He made the boundaries look quite small, which they certainly are not! I knew I'd bobbled the catch but I thought I'd squeezed it in the chest. It was a bit embarrassing but it is one of those things."
'England smarter than in the past'
Ravi Bopara
Former England all-rounder on BBC Test Match Special
This is a bit more of a smarter, versatile England side than we have had in the past, maybe 10 years back. You saw the way they bowled at the end, they used the big boundary wisely.
They didn't just stick to what they know, they dug the ball into the pitch and made New Zealand hit out to the big boundary.
It was really well set up by the batters up top. They went hard and that's what I loved about it. It doesn't matter if it is Trent Boult or whoever bowling, just take them on.
Post update
England captain and player of the match Jos Buttler: "I said at the toss you don't become a bad team overnight. We had a bad performance but we know we've got great players in our line-up so there was still lots of confidence in the group and we left it all out there tonight.
"It is a ruthless tournament. Last year we saw South Africa go out having won four out of five games, so it can be tough to get through.
"But now we know it's all in our hands and you expect to be under pressure in World Cup cricket, that's what it's all about.
"With our line-up, we bat deep and it allows me to take it on maybe an over earlier than you normally would. The wicket was tricky, it was tough against the spin, but Alex Hales played really well at the other end to get us on our way and it took the pressure off me.
"We are going to keep being flexible with the batting order, the game shapes up in different ways and we were finding the spin tough so it was good to get a left-hander (Moeen Ali) in early.
On becoming England's leading T20 run-scorer: "It's a nice feeling, it's always nice to look at your individual performances but I'm just trying to do my job on the day and do my best for the team."
More from Sam Curran, on not playing since the loss to Ireland: "It was a weird game at the start because we haven't played in so long but once we got into it, the fans were amazing and all that stuff gets you going again. Now we'll be really confident for Saturday (against Sri Lanka)."
On his bowling: "Tonight was a pitch that maybe suited the spinners a bit more and I felt my variations could come in handy. We used the dimensions really well, particularly when Glenn Phillips was going really well.
"We knew it was going to be close, to win by 20 runs is great and helps the net run-rate, which we know is going to be a factor."
'Another must-win game on Saturday'
England all-rounder Sam Curran, speaking to Test Match Special: "I think it was a really important game, we knew it was going to be close because New Zealand are a really good side.
"We chose to bat first and I think the guys batted beautifully. Jos and Hales at the top and then the other guys chipped in. It felt like we hadn't played in a while because of all the rain and travel - but what a great win against a New Zealand playing well.
"Now we travel to Sydney for another must-win game against Sri Lanka."
Post update
For the record, New Zealand will need to beat Ireland to ensure they go through. If they lose or are washed out, they can be overtaken by England, Australia and Sri Lanka.
Live Reporting
Stephan Shemilt and Callum Matthews
All times stated are UK
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Latest PostPost update
You can read Matthew Henry's report from the Gabba here.
England are still in this World Cup. Next stop is a Saturday showdown with Sri Lanka in Sydney.
Bye for now.
Post update
So it's eyes down for Friday and Saturday. Before then, attention switches to Group Two, where it looks like a three-way scrap between India, Bangladesh and South Africa.
Post update
More from England captain Jos Buttler: "We've had a lot of success batting first, it's something we want to be brave with and take that option sometimes. It's definitely an aggressive option and it was the right one today.
On Alex Hales: "He played brilliantly. We know what he's capable of, he's taken his chance to get back in the side.
"You have to be patient in T20 cricket, it's easy to critique and write people off after a few low scores but you're asking people to play a high-risk game. You've got to give them that safety net and encourage them to keep taking the game on.
On Adil Rashid: "I feel for him a bit, Adil has been bowling really well without the rewards that he's probably deserved. He had some tough luck with his best mate dropping one off him today but he's going to take plenty of wickets for us going forward, no doubt."
Post update
I'm really sorry to say this, but I can't shake an uneasy feeling about England needing to beat the Chris Silverwood-led Sri Lanka to go through.
Post update
To mark your card, the Ireland-New Zealand and Australia-Afghanistan games are both in Adelaide on Friday.
England play Sri Lanka in Sydney on Saturday knowing exactly what they have to do.
'England bowled better than us'
New Zealand's Glenn Phillips, speaking on Test Match Special: "It's a tough one. When a team gets 179, you're either going to get really close or nowhere near I reckon. We gave it our best shot but they bowled really well and were the better team today.
"I think on a big ground, trying to chasing 16s in the last three overs is tough. We had our plans in mind and tried to take it as deep and as close as possible but the way England stuck to their bowling plans made it tough for us to have any massive overs.
"It's a real credit to how the England boys bowled."
'England impressive from ball one'
Ben Cutting
Former Australia all-rounder on BBC Test Match Special
England were impressive and it started from ball one and the way they took on the powerplay with Alex Hales. We've seen a number of innings on this pitch now and we thought a par total was about 150 or 160, and they went well past that.
That win can provide England with the momentum that they need.
'The guys closed the game out beautifully'
England all-rounder Sam Curran on Sky Sports: "The decision to bat first was something that Jos wanted to do so we could get out there and at them, on a wicket that looked quite tricky.
"There is no panic. We went wrong in the Ireland game, and we knew New Zealand are a good team and I thought with three or four overs to go that I'd be having to defend 10 in the last game but the guys closed the game out beautifully at the end.
"The dimensions are big so we knew if guys are hitting for six they have to play a really good shot. We had our plans but Glenn Phillips got going and made it tough. He is a quality player and his confidence is really high. They are an amazing team and if we go well on Saturday we might have to face them again, you never know."
'Hats off to England, they were clinical'
New Zealand captain Kane Williamson: "Credit to the way England played. They put us under pressure from the get-go with the bat and we struggled to get the breakthroughs to change the momentum. It was a tough surface, but they played beautifully. We were in the game second half and we needed a few things to go our way but hats off to England, they were clinical.
"They were probably above par but it is what it is. We were just trying to take it deep and we had our moments but we weren't able to get ahead of the game. Credit to the way they bowled - it was tricky with the big boundaries.
"Jos is one of the best players in the world so you don't want to drop him twice and he'll probably make you play. He made the boundaries look quite small, which they certainly are not! I knew I'd bobbled the catch but I thought I'd squeezed it in the chest. It was a bit embarrassing but it is one of those things."
'England smarter than in the past'
Ravi Bopara
Former England all-rounder on BBC Test Match Special
This is a bit more of a smarter, versatile England side than we have had in the past, maybe 10 years back. You saw the way they bowled at the end, they used the big boundary wisely.
They didn't just stick to what they know, they dug the ball into the pitch and made New Zealand hit out to the big boundary.
It was really well set up by the batters up top. They went hard and that's what I loved about it. It doesn't matter if it is Trent Boult or whoever bowling, just take them on.
Post update
England captain and player of the match Jos Buttler: "I said at the toss you don't become a bad team overnight. We had a bad performance but we know we've got great players in our line-up so there was still lots of confidence in the group and we left it all out there tonight.
"It is a ruthless tournament. Last year we saw South Africa go out having won four out of five games, so it can be tough to get through.
"But now we know it's all in our hands and you expect to be under pressure in World Cup cricket, that's what it's all about.
"With our line-up, we bat deep and it allows me to take it on maybe an over earlier than you normally would. The wicket was tricky, it was tough against the spin, but Alex Hales played really well at the other end to get us on our way and it took the pressure off me.
"We are going to keep being flexible with the batting order, the game shapes up in different ways and we were finding the spin tough so it was good to get a left-hander (Moeen Ali) in early.
On becoming England's leading T20 run-scorer: "It's a nice feeling, it's always nice to look at your individual performances but I'm just trying to do my job on the day and do my best for the team."
Post update
Post update
More from Sam Curran, on not playing since the loss to Ireland: "It was a weird game at the start because we haven't played in so long but once we got into it, the fans were amazing and all that stuff gets you going again. Now we'll be really confident for Saturday (against Sri Lanka)."
On his bowling: "Tonight was a pitch that maybe suited the spinners a bit more and I felt my variations could come in handy. We used the dimensions really well, particularly when Glenn Phillips was going really well.
"We knew it was going to be close, to win by 20 runs is great and helps the net run-rate, which we know is going to be a factor."
'Another must-win game on Saturday'
England all-rounder Sam Curran, speaking to Test Match Special: "I think it was a really important game, we knew it was going to be close because New Zealand are a really good side.
"We chose to bat first and I think the guys batted beautifully. Jos and Hales at the top and then the other guys chipped in. It felt like we hadn't played in a while because of all the rain and travel - but what a great win against a New Zealand playing well.
"Now we travel to Sydney for another must-win game against Sri Lanka."
Post update
For the record, New Zealand will need to beat Ireland to ensure they go through. If they lose or are washed out, they can be overtaken by England, Australia and Sri Lanka.
From the press box...
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Here's the table. Have you done that NRR calculation yet?
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Jos Buttler is player of the match. His batting, keeping and captaincy was excellent.
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Post update
England go second, above the Aussies. Their advantage in NRR is about 0.8 of a run, which is sizeable.
Someone more clever than me will work out what that means for both sides going into the final round of group matches.