ICC Men's World Cup, Kolkata
South Africa 212 (49.4 overs): Miller 101 (116), Klaasen 47 (48); Starc 3-34
Australia 215-7 (47.2 overs): Head 62 (48); Shamsi 2-42
Australia won by three wickets
Australia are through to the World Cup final after a tension-filled three-wicket win over South Africa in Kolkata.
After bowling South Africa out for 212, Pat Cummins' side made a flying start with Travis Head hitting a quickfire 62 before they were pegged back by the Proteas spinners and slipped to 137-5.
Australia edged closer but lost their seventh wicket with 20 runs still needed and although the pressure continued to build, Cummins and Mitchell Starc kept their cool to complete a hard-fought victory with 16 balls to spare.
The Proteas had been reduced to 24-4 following superb new-ball bursts from Josh Hazlewood and Starc before David Miller rescued the innings with a determined 101 from 116 balls.
But despite a valiant effort in the field, it wasn't enough and Australia advance to face India in Sunday's final in Ahmedabad.
Batting first in overcast conditions was a risk South Africa were willing to take given their previous success with that approach but they were soon in trouble as Starc and Hazlewood tore through the top order.
Starc removed Temba Bavuma in the first over, Quinton de Kock fell to Hazlewood in the sixth and with Australia energised in the field, South Africa had just eight on the board after seven overs and were 18-2 at the end of the powerplay.
When Aiden Markram and Rassie van der Dussen fell in successive overs, it was left to Miller and Heinrich Klaasen to salvage the innings and, either side of a 40-minute rain delay, the pair did just that with a composed 95-run stand.
Klaasen fell for 47 but Miller kept going, reaching his sixth one-day international hundred with his fifth sixth before holing out from the next legal delivery.
Head and David Warner looked like knocking the runs off in a hurry, adding 60 in the first six overs, and even when the latter was bowled by Markram, the runs kept coming for Australia.
South Africa's seamers were taking some punishment and Head, dropped on 40, hit three consecutive boundaries to bring up his half-century.
The introduction of spin changed the game. Keshav Maharaj bowled Head through the gate for 62 and Tabraiz Shamsi accounted for Marnus Labuschagne and Glenn Maxwell to bring the Proteas right back into contention.
Josh Inglis and Steve Smith prevented a collapse but with the finish line in sight for Australia, Coetzee bounced out Smith and then bowled Inglis.
With South Africa refusing to know when they were beaten, Starc and Cummins had to bide their time and more than seven overs went by before the Australia skipper cut Marco Jansen for four to seal the win.
South Africa fail to recover from early collapse
Even under gloomy skies and with captain Bavuma admitting he was not fully fit, it was no surprise South Africa chose to bat first.
They have been every bit as dominant setting a total as they have been jittery chasing at this World Cup.
Inside the first 12, though, they saw their hitherto hugely effective plan picked apart by Starc and Hazlewood.
The bowling and fielding was of the highest quality and South Africa's top order simply could not withstand the pressure.
But, for a side infamous for crumbling in high-pressure games in years gone by, they showed impressive fight with both bat and ball.
Miller and Klaasen stood tall in the face of some intense Australia pressure to ensure South Africa at least had a total to defend.
They could then have wilted with the ball after a horrendous start but instead their resilience shone through with their grit and determination on full display in the form of Coetzee, who powered through an eight-over spell to take the game deep.
Ultimately, though, their early collapse cost them. Another 30 runs may have been enough. But, as it is, for all the spirit they showed, the wait to reach a men's World Cup final goes on.
Australia hold firm to give themselves a shot at glory
Six weeks have gone by but Australia's World Cup will end as it began, going head-to-head with a formidable India side.
The venue has changed but the challenge facing them remains the same as they take on a team with no obvious weaknesses in their home conditions, in front of a packed-house, 99.9% of whom will be supporting India.
But while the challenge is the same, Australia themselves are not. They have grown into this tournament since the six-wicket defeat in Chennai and after eight wins on the bounce, confidence will be high.
This is what Australia do at World Cups. They win.
As hard as they made it for themselves against South Africa, they got the job done. The talent at their disposal was clear at the start of both innings and their experience came through at the death.
Australia have avenged one of their two losses at this tournament in the semis and, even up against the might of India, they will be backing themselves to make up for the other in the final.
'Australia were ruthless' - what they said
Australia captain Pat Cummins: "I think it is easier out there than sitting in the dug-out. A nerve-wracking couple of hours. Great effort, plenty of good performances. We're pretty pumped.
"It's going to be a special final. I still talk of the 2015 final as one of my career highlights and I wasn't even playing. So to be out there in a final, in India, world's biggest stadium... it's a very happy changing room at the moment."
South Africa captain Temba Bavuma: "Our character came through. We showed the resilience we talk about and a bit of dog fight. The way we started with the bat and ball was the turning point, we always had to play catch-up.
"The conditions combined with the quality of the Australia attack. They were ruthless and exploited every bit of advantage, and really put us under pressure. From 24-4, it was always going to be hard to get a competitive total."
Player of the match, Australia's Travis Head: "It's hard to unpack all of that. I didn't move for the past couple of hours. It was a tense finish and an amazing game.
"We knew how it was going to play and how we would adapt. You train, go to bed and think about it.
"We knew it would be a grind and a battle and that's what it was."