So Australia join England, India and South Africa in Thursday's semi-finals.

They look to be hitting form at the right time.

We'll find out who plays who in the last four once Group B is completed on Friday. Join us for both matches from 04:00 GMT on Tuesday.

Scroll down for reaction and highlights from Australia's crucial win. Click here for full details.

New Zealand always hung in in a difficult chase but were never on top.

20-year-old leg-spinner Georgia Wareham was the star bowler for Australia with the three big wickets of Sophie Devine, Suzie Bates and Maddy Green.

Australia also got a boost late in their innings from Perry and Rachel Haynes. The hosts scored 33 from their final three overs. Perry scored 21 from 15 and Haynes 19 from eight. Those cameos proved crucial.

New Zealand skipper Sophie Devine admitted Australia scored a few too many in their innings.

Beth Mooney's knock of 60 from 50 balls was the key. It was a fine innings with six fours and two sixes.

The one concern for Australia was that their star all-rounder Ellyse Perry pulled up with what looked to be a hamstring injury.

She had been a doubt for this game with a hip problem and did not return to the field after limping off.

Here's what her skipper Meg Lanning had to say at the presentation...

"I haven't heard anything. It didn't look great. She is tough player. Hopefully she is OK."

Australia captain Meg Lanning: "It was a crunch game and we handled it very well. Beth Mooney batted excellently and gave us a really good base. She showed today what a really good player she is.

"We back all of our players. For Georgia [Wareham] to come in and bowl so well is a credit to her.

"The Bangladesh game was a turning point for us. We played lot more like how we play. We are looking forward to our next challenge.

"We were calm when under the pump and did the basics well. It gives us a lot of confidence going into the semi-final."

New Zealand captain Sophie Devine: "You can always go back over the 120 balls and find something you could do better. Credit to Australia, they're a great team and I wish them well going forward."

As it stands England are top of Group B and would therefore meet Australia in the semi-finals.

But South Africa still have one game to play and will overtake England if they beat West Indies tomorrow.

Were that to happen England would play unbeaten India in the last four.

The four semi-finalists will be Australia, India, South Africa and England.

Who plays who will become clear after the final matches in Group B tomorrow.

Australia's Georgia Wareham, who took 3-17: "I felt like I had a bit of confidence from the way I started my overs. The nerves were high before this game so it's good to be in the semi-finals. it's not job done yet though."

Wareham is beaming when Nasser Hussain points out at the presentation that Australia now have a semi-final at the SCG coming up.

Wareham is named player of the match. The right decision.

New Zealand gave it a good go and were in the chase at times but Australia always found wickets when they had to.

Georgia Wareham with the big wickets of Sophie Devine, Susie Bates and Maddy Green won it for Australia.

Kristen Beams
Ex-Australia leg-spinner on BBC Test Match Special

It was a superb all-round performance by Australia. They'll be pleased to put in that performance under pressure.

The finish is a bit of a shambles with Nic Carey dropping a catch on the boundary rope. We then have to check if the ball went for six.. It did. It's six runs but all that matters is Australia win.

The hosts reach their semi-finals of their home World Cup.

Katey Martin finds the boundary and has played a good hand but it's not going to be enough.

Australia are going to the semi-finals. New Zealand need 15 from the final two balls but they're already cheering in the stands.

Just a dot. 17 from three balls.

Gardner is darting it in. The crowd are applauding. They know it's all over. 18 from four to win.

Kasperek steps across her stumps and gets a fair bit of bat on a sweep but picks out the fielder on the bounce at fine leg.

19 from five balls needed.