This result makes tomorrow's encounter between New Zealand and Pakistan very significant.
Afghanistan will be hoping that New Zealand lose - but if they win, it will see England, Sri Lanka, Netherlands and Pakistan officially eliminated.
We'll have live radio coverage of that game from 05:00 GMT, followed by another big fixture in England v Australia, with that live text starting at 08:00.
We look forward to you joining us for another busy day tomorrow!
Post update
Here is the moment that Afghanistan captain Hashmatullah Shahidi hit the winning boundary.
They are having a brilliant run in this World Cup and as he said in his interview, they are still "dreaming".
Post update
Abhishek Jhunjhunwala
Former IPL batter on BBC Test Match Special
I'd hope Afghanistan go all the way, it'd be the best story in a long time. They've played their hearts out, it's been a top performance, let's hope they get into that top four and I think they've got the ability to do that.
Post update
Afghanistan captain Hashmatullah Shahidi: "The fielding and the run chase are both equally pleasing. It is the third time now that we have chased and achieved a target.
"We like to have a target and that helps us play accordingly because we know what we need to do and the situation is clearer for us.
"Mohammad Nabi is a special player. He is so talented and he loves to take responsibility with the ball like he did today.
"We have good team unity. We are very united and we are always playing for the team and winning for the team.
"We are still dreaming and we are still trying our best to make the semi-final. That would be such a big achievement for our country and for me.
"A message to our country back home. We know that people are struggling, we are with them. I dedicate this win to them."
'We'll have to re-group for England'
Netherlands captain Scott Edwards: "The run-outs were hard to come back from, we set ourselves up for a good total. They have quality spinners through the middle and we didn't have our top order batters to face them.
"We've done well batting first, defending scores. We thought if we scored 280 we'd be well in the game.
"We weren't thinking about the Champions Trophy before this game, our attention will probably turn to that. We'll have to re-group for that England game."
Post update
The Netherlands chipped in with a couple of wickets but their only chance of victory was to take them in clusters. Afghanistan batted patiently, sensibly and got themselves over the line without any risk.
Post update
Abhishek Jhunjhunwala
Former IPL batter on BBC Test Match Special
Afghanistan have a clarity of thought that was missing in previous tournaments. That's come from Jonathan Trott. That's the biggest change - there numbers 3-6 have really contributed, even when they've been under pressure they haven't crumbled.
Post update
Lydia Greenway
Former England batter on BBC Test Match Special
The Netherlands looked like they were going nicely, Mujeeb was trying to over compensate and runs were flowing freely. But the story of their innings was the number of run outs, which meant they were unable to make a defendable total.
Post update
The Netherlands started their innings really nicely, Max O'Dowd and Colin Ackermann steering them to 73-1.
But what followed was absolute chaos and they can't argue with the fact that they threw it away. Four of their top five were run out, and they never recovered, eventually slumping to 179 all out.
Afghanistan were brilliant in the field, but the run outs were avoidable.
Post update
Player of the match, Afghanistan bowler Mohammad Nabi: "When I'm bowling, I'm just focusing on my line and lengths and bowling as many dot balls as I can. That makes the batters rush and my consistency helps me be successful.
"I am happy with how my plans worked today.
"I'm still working on my fitness, my body is working fine and I still love playing for Afghanistan!"
Post update
It was a straightforward victory in the end, with seven wickets in hand and just under 19 overs remaining.
Captain Hashmatullah Shahidi finishes unbeaten on 56, while Rahmat Shah earlier hit 52.
Former England batter and now Afghanistan coach Jonathan Trott is full of smiles now, shaking hands and hugging all his players as they leave the pitch with big grins on their faces.
Post update
Aatif Nawaz
BBC Test Match Special commentator
Hashmat holds up one finger, he might as well hold up four as that's how many games Afghanistan have now won in this World Cup.
BreakingAfghanistan win by seven wickets
Crunched for four, and the Afghanistan celebrations begin!
Fittingly, the captain hits the winning runs and points to his team-mates in satisfaction.
Afghanistan keep their name in contention for a semi-final spot, with four wins out of seven so far.
How's stat?!
Andy Zaltzman
Cricket statistician on Test Match Special
We haven't had a completed World Cup match without a six since the 2015 World Cup quarter-final between South Africa and Sri Lanka. That's 80 matches.
Afg 176-3
Need 4 runs to win
Six runs come from Colin Ackermann's over with minimal risk, and it's just a matter of time now for Afghanistan.
Can they win it in style?
50 for Hashmatullah Shahidi
Afg 173-3
The Afghanistan skipper brings up a composed half-century, executing his job to perfection and he's ready to steer his side to victory.
He reaches it from 59 balls, shares a hug with Azmatullah at the other end, but gets back to work quickly.
Post update
Aatif Nawaz
BBC Test Match Special commentator
You can't say they haven't earned it, it's been a top-notch performance from Afghanistan, they've been all over the Netherlands.
Afg 170-3
Need 10 runs to win
Aryan Dutt gifts Azmatullah a freebie, a full toss that the batter can easily whack down the ground for four.
A single then takes Afghanistan to within just 10 runs of what has been, for the most part, an easy win.
Not out
Nothing to see here. Azmatullah's foot was firmly on the ground.
Post update
Abhishek Jhunjhunwala
Former IPL batter on BBC Test Match Special
He was standing on his back foot, how can he be stumped? Unless he jumped in the air - he was trying a back foot cut.
Live Reporting
Ffion Wynne, Mike Peter and Tom Mallows
All times stated are UK
Latest PostPost update
This result makes tomorrow's encounter between New Zealand and Pakistan very significant.
Afghanistan will be hoping that New Zealand lose - but if they win, it will see England, Sri Lanka, Netherlands and Pakistan officially eliminated.
We'll have live radio coverage of that game from 05:00 GMT, followed by another big fixture in England v Australia, with that live text starting at 08:00.
Until then, here's Tom Mallows' match report from today.
We look forward to you joining us for another busy day tomorrow!
Post update
Here is the moment that Afghanistan captain Hashmatullah Shahidi hit the winning boundary.
They are having a brilliant run in this World Cup and as he said in his interview, they are still "dreaming".
Post update
Abhishek Jhunjhunwala
Former IPL batter on BBC Test Match Special
I'd hope Afghanistan go all the way, it'd be the best story in a long time. They've played their hearts out, it's been a top performance, let's hope they get into that top four and I think they've got the ability to do that.
Post update
Afghanistan captain Hashmatullah Shahidi: "The fielding and the run chase are both equally pleasing. It is the third time now that we have chased and achieved a target.
"We like to have a target and that helps us play accordingly because we know what we need to do and the situation is clearer for us.
"Mohammad Nabi is a special player. He is so talented and he loves to take responsibility with the ball like he did today.
"We have good team unity. We are very united and we are always playing for the team and winning for the team.
"We are still dreaming and we are still trying our best to make the semi-final. That would be such a big achievement for our country and for me.
"A message to our country back home. We know that people are struggling, we are with them. I dedicate this win to them."
'We'll have to re-group for England'
Netherlands captain Scott Edwards: "The run-outs were hard to come back from, we set ourselves up for a good total. They have quality spinners through the middle and we didn't have our top order batters to face them.
"We've done well batting first, defending scores. We thought if we scored 280 we'd be well in the game.
"We weren't thinking about the Champions Trophy before this game, our attention will probably turn to that. We'll have to re-group for that England game."
Post update
The Netherlands chipped in with a couple of wickets but their only chance of victory was to take them in clusters. Afghanistan batted patiently, sensibly and got themselves over the line without any risk.
Post update
Abhishek Jhunjhunwala
Former IPL batter on BBC Test Match Special
Afghanistan have a clarity of thought that was missing in previous tournaments. That's come from Jonathan Trott. That's the biggest change - there numbers 3-6 have really contributed, even when they've been under pressure they haven't crumbled.
Post update
Lydia Greenway
Former England batter on BBC Test Match Special
The Netherlands looked like they were going nicely, Mujeeb was trying to over compensate and runs were flowing freely. But the story of their innings was the number of run outs, which meant they were unable to make a defendable total.
Post update
The Netherlands started their innings really nicely, Max O'Dowd and Colin Ackermann steering them to 73-1.
But what followed was absolute chaos and they can't argue with the fact that they threw it away. Four of their top five were run out, and they never recovered, eventually slumping to 179 all out.
Afghanistan were brilliant in the field, but the run outs were avoidable.
Post update
Player of the match, Afghanistan bowler Mohammad Nabi: "When I'm bowling, I'm just focusing on my line and lengths and bowling as many dot balls as I can. That makes the batters rush and my consistency helps me be successful.
"I am happy with how my plans worked today.
"I'm still working on my fitness, my body is working fine and I still love playing for Afghanistan!"
Post update
It was a straightforward victory in the end, with seven wickets in hand and just under 19 overs remaining.
Captain Hashmatullah Shahidi finishes unbeaten on 56, while Rahmat Shah earlier hit 52.
Former England batter and now Afghanistan coach Jonathan Trott is full of smiles now, shaking hands and hugging all his players as they leave the pitch with big grins on their faces.
Post update
Aatif Nawaz
BBC Test Match Special commentator
Hashmat holds up one finger, he might as well hold up four as that's how many games Afghanistan have now won in this World Cup.
BreakingAfghanistan win by seven wickets
Crunched for four, and the Afghanistan celebrations begin!
Fittingly, the captain hits the winning runs and points to his team-mates in satisfaction.
Afghanistan keep their name in contention for a semi-final spot, with four wins out of seven so far.
How's stat?!
Andy Zaltzman
Cricket statistician on Test Match Special
We haven't had a completed World Cup match without a six since the 2015 World Cup quarter-final between South Africa and Sri Lanka. That's 80 matches.
Afg 176-3
Need 4 runs to win
Six runs come from Colin Ackermann's over with minimal risk, and it's just a matter of time now for Afghanistan.
Can they win it in style?
50 for Hashmatullah Shahidi
Afg 173-3
The Afghanistan skipper brings up a composed half-century, executing his job to perfection and he's ready to steer his side to victory.
He reaches it from 59 balls, shares a hug with Azmatullah at the other end, but gets back to work quickly.
Post update
Aatif Nawaz
BBC Test Match Special commentator
You can't say they haven't earned it, it's been a top-notch performance from Afghanistan, they've been all over the Netherlands.
Afg 170-3
Need 10 runs to win
Aryan Dutt gifts Azmatullah a freebie, a full toss that the batter can easily whack down the ground for four.
A single then takes Afghanistan to within just 10 runs of what has been, for the most part, an easy win.
Not out
Nothing to see here. Azmatullah's foot was firmly on the ground.
Post update
Abhishek Jhunjhunwala
Former IPL batter on BBC Test Match Special
He was standing on his back foot, how can he be stumped? Unless he jumped in the air - he was trying a back foot cut.