And that's all from us today. We'll be back tomorrow with another double-game day, starting with Australia v Bangladesh at 5:00 GMT and followed by England v Pakistan at 8:30 GMT.
South Africa captain Temba Bavuma: "My leg is sore. I don't know the extend of it yet but I'll have to be fine. I am stubborn, it will have to be fine.
"I could have not batted, but I want to be out there for my team. It was an opportunity to get time in the middle that I didn't want to miss. And leading this team is so important to me, to marshal the bowlers and keep building that, so I felt it was the right decision to stay out there.
"Winning is a habit so we want to take that momentum into the semi-finals and we will take a lot of confidence from this result. Normally we want to bat first but we wanted to bat second today, something a little different, and to get over the line will help us going forward.
"It was a fantastic knock by Rassie to take ownership and responsibility of the chase, and everyone else played around him.
"We can always learn and improve in different areas but we will take the win and take the momentum.
"Yes, part of me is dreaming. We want to be back here [in the final]. But Australia are a big hurdle for us to overcome. We will enjoy today, take the learnings, and then get our minds set on that game."
Post update
Andile Phehlukwayo finished the game in style in his first outing of the tournament after a twitchy start.
Post update
Afghanistan captain Hashmatullah Shahidi: "As a captain, I'm quite happy with the performance. We fought from the beginning to the last moment in every game. Good matches and good learning for the future.
"I'm proud of our batsmen in this tournament. We were struggling before, so we sat together and talked about the weak points, and at the end you saw the results. It's a positive thing for us, looking to the future. Everyone knows we have a good spin department, if we go with the same momentum we will be a very good side in the future.
"I think we gave a good message to the world in this tournament. We played big teams and we fought. The Australia game was in our hands, it was a shock that defeat. There was a lot of learning."
Post update
There are plenty of positives for South Africa to take into their semi-final. The form of Keshav Maharaj and Gerald Coetzee with the ball is a huge boost, finishing with 2-25 and 4-44 respectively today.
But there were injuries to Lungi Ngidi and Temba Bavuma, which could see a re-jig to the line-up if they do not recover in time.
Post update
Player of the Match Rassie van der Dussen: "We weren't unhappy with bowling first, we wanted to do that and get chasing. They are a quality attack, especially their spinners, so I think getting ourselves into a tough position like that and getting through it was a good thing.
"Someone always has to play the anchor role in a chase and I was happy to do that. The platform I had from Temba and Quinton made my job a lot easier, too.
"We do so well batting first, and that makes people think we chase badly. We would like to improve our chasing, yes, and I think being in that situation tonight will hold us in good stead.
"We've learned a lot from this game and the India loss. We know what to expect in our semi-final."
Post update
Rassie van der Dussen is named player of the match for his unbeaten 76 in victory. We will hear from him shortly.
There was another brilliant performance with the bat earlier from Azmatullah Omarzai, who finished 97 not out in Afghanistan's 244.
Renowned for their spinners, it's been good to see Afghanistan's batting develop and challenge the top teams.
Post update
Carlos Brathwaite
Ex-West Indies all-rounder on BBC Test Match Special
Afghanistan might regret the loss to Bangladesh, if they'd faced them now instead of South Africa you'd back them to defeat them and put themselves in a position to qualify.
Post update
So South Africa head into next week's semi-final with a confidence boost, getting another win while chasing.
There was a slight wobble when David Miller fell tamely to leave them 182-5, but Phehlukwayo and Van der Dussen calmly negotiated the tricky period of spin and cruised it in the end.
A tough end to the World Cup for Afghanistan, but a brave effort and a very promising campaign for them.
Post update
Carlos Brathwaite
Ex-West Indies all-rounder on BBC Test Match Special
Van der Dussen got them to a position where pace had to come back on, then Phehlukwayo finished it with 6-4-6.
Post update
Natalie Germanos
BBC Test Match Special commentator
He says "enough of this" and finishes it off with a six!
BreakingSOUTH AFRICA WIN BY FIVE WICKETS
Sealed with a six!
After a tentative start against the spinners, Andile Phehlukwayo goes six, four, six to whack the remaining runs in style.
He finishes with 33 not out - a very handy performance having come in at a tricky position, and in his first appearance of the tournament.
Rassie van der Dussen finishes 76 not out, anchoring the innings and finally, another successful chase.
Post update
Carlos Brathwaite
Ex-West Indies all-rounder on BBC Test Match Special
He's fought through a tough period and is hitting the ball so beautifully off the pace.
SA 241-5
Need 4 runs to win
Crashed through the covers for four!
Now he wants this done in a hurry!
Post update
Carlos Brathwaite
Ex-West Indies all-rounder on BBC Test Match Special
Super shot. The positions he's getting into, if he gets one in his zone you're backing. He never had any intention to hit it for four, he always wanted to hit it for six.
SA 237-5
Need 8 runs to win
Nerves? None.
Andile Phehlukwayo whacks the first ball from Naveen's over for six!
Post update
With 14 runs required, what better time for a drinks' break?
Post update
Natalie Germanos
BBC Test Match Special commentator
This is Van der Dussen's wheelhouse, when he gets to 50 he tends to accelerate. With the run rate not too big, he's comfortable finding the gaps and rotating the strike.
SA 231-5
Need 14 from 18 balls
Noor Ahmad, Afghanistan's last threatening spinner, twirls his way through his ninth over but Van der Dussen and Phehlukwayo easily take nine from it.
After David Miller's wicket, it was bubbling quite nicely but these two have withstood the pressure and it's been relatively calm since then.
Post update
Carlos Brathwaite
Ex-West Indies all-rounder on BBC Test Match Special
It felt like Phehlukwayo was trying to ride out the spinners, now it's time to cash in.
Live Reporting
Mike Peter
All times stated are UK
Latest PostPost update
And that's all from us today. We'll be back tomorrow with another double-game day, starting with Australia v Bangladesh at 5:00 GMT and followed by England v Pakistan at 8:30 GMT.
For now, here's Sam Drury's match report for you to enjoy.
We look forward to you joining us tomorrow!
'Part of me is dreaming'
South Africa captain Temba Bavuma: "My leg is sore. I don't know the extend of it yet but I'll have to be fine. I am stubborn, it will have to be fine.
"I could have not batted, but I want to be out there for my team. It was an opportunity to get time in the middle that I didn't want to miss. And leading this team is so important to me, to marshal the bowlers and keep building that, so I felt it was the right decision to stay out there.
"Winning is a habit so we want to take that momentum into the semi-finals and we will take a lot of confidence from this result. Normally we want to bat first but we wanted to bat second today, something a little different, and to get over the line will help us going forward.
"It was a fantastic knock by Rassie to take ownership and responsibility of the chase, and everyone else played around him.
"We can always learn and improve in different areas but we will take the win and take the momentum.
"Yes, part of me is dreaming. We want to be back here [in the final]. But Australia are a big hurdle for us to overcome. We will enjoy today, take the learnings, and then get our minds set on that game."
Post update
Andile Phehlukwayo finished the game in style in his first outing of the tournament after a twitchy start.
Post update
Afghanistan captain Hashmatullah Shahidi: "As a captain, I'm quite happy with the performance. We fought from the beginning to the last moment in every game. Good matches and good learning for the future.
"I'm proud of our batsmen in this tournament. We were struggling before, so we sat together and talked about the weak points, and at the end you saw the results. It's a positive thing for us, looking to the future. Everyone knows we have a good spin department, if we go with the same momentum we will be a very good side in the future.
"I think we gave a good message to the world in this tournament. We played big teams and we fought. The Australia game was in our hands, it was a shock that defeat. There was a lot of learning."
Post update
There are plenty of positives for South Africa to take into their semi-final. The form of Keshav Maharaj and Gerald Coetzee with the ball is a huge boost, finishing with 2-25 and 4-44 respectively today.
But there were injuries to Lungi Ngidi and Temba Bavuma, which could see a re-jig to the line-up if they do not recover in time.
Post update
Player of the Match Rassie van der Dussen: "We weren't unhappy with bowling first, we wanted to do that and get chasing. They are a quality attack, especially their spinners, so I think getting ourselves into a tough position like that and getting through it was a good thing.
"Someone always has to play the anchor role in a chase and I was happy to do that. The platform I had from Temba and Quinton made my job a lot easier, too.
"We do so well batting first, and that makes people think we chase badly. We would like to improve our chasing, yes, and I think being in that situation tonight will hold us in good stead.
"We've learned a lot from this game and the India loss. We know what to expect in our semi-final."
Post update
Rassie van der Dussen is named player of the match for his unbeaten 76 in victory. We will hear from him shortly.
There was another brilliant performance with the bat earlier from Azmatullah Omarzai, who finished 97 not out in Afghanistan's 244.
Renowned for their spinners, it's been good to see Afghanistan's batting develop and challenge the top teams.
Post update
Carlos Brathwaite
Ex-West Indies all-rounder on BBC Test Match Special
Afghanistan might regret the loss to Bangladesh, if they'd faced them now instead of South Africa you'd back them to defeat them and put themselves in a position to qualify.
Post update
So South Africa head into next week's semi-final with a confidence boost, getting another win while chasing.
There was a slight wobble when David Miller fell tamely to leave them 182-5, but Phehlukwayo and Van der Dussen calmly negotiated the tricky period of spin and cruised it in the end.
A tough end to the World Cup for Afghanistan, but a brave effort and a very promising campaign for them.
Post update
Carlos Brathwaite
Ex-West Indies all-rounder on BBC Test Match Special
Van der Dussen got them to a position where pace had to come back on, then Phehlukwayo finished it with 6-4-6.
Post update
Natalie Germanos
BBC Test Match Special commentator
He says "enough of this" and finishes it off with a six!
BreakingSOUTH AFRICA WIN BY FIVE WICKETS
Sealed with a six!
After a tentative start against the spinners, Andile Phehlukwayo goes six, four, six to whack the remaining runs in style.
He finishes with 33 not out - a very handy performance having come in at a tricky position, and in his first appearance of the tournament.
Rassie van der Dussen finishes 76 not out, anchoring the innings and finally, another successful chase.
Post update
Carlos Brathwaite
Ex-West Indies all-rounder on BBC Test Match Special
He's fought through a tough period and is hitting the ball so beautifully off the pace.
SA 241-5
Need 4 runs to win
Crashed through the covers for four!
Now he wants this done in a hurry!
Post update
Carlos Brathwaite
Ex-West Indies all-rounder on BBC Test Match Special
Super shot. The positions he's getting into, if he gets one in his zone you're backing. He never had any intention to hit it for four, he always wanted to hit it for six.
SA 237-5
Need 8 runs to win
Nerves? None.
Andile Phehlukwayo whacks the first ball from Naveen's over for six!
Post update
With 14 runs required, what better time for a drinks' break?
Post update
Natalie Germanos
BBC Test Match Special commentator
This is Van der Dussen's wheelhouse, when he gets to 50 he tends to accelerate. With the run rate not too big, he's comfortable finding the gaps and rotating the strike.
SA 231-5
Need 14 from 18 balls
Noor Ahmad, Afghanistan's last threatening spinner, twirls his way through his ninth over but Van der Dussen and Phehlukwayo easily take nine from it.
After David Miller's wicket, it was bubbling quite nicely but these two have withstood the pressure and it's been relatively calm since then.
Post update
Carlos Brathwaite
Ex-West Indies all-rounder on BBC Test Match Special
It felt like Phehlukwayo was trying to ride out the spinners, now it's time to cash in.