Australia will face hosts India in Sunday's World Cup final after a nervy last-four victory over South Africa in Kolkata.
The match at Eden Gardens on Thursday looked set for a quick finish after South Africa were bowled out for 212 with David Miller's defiant 101 the saving grace for the Proteas.
Australia then surged to 60 without loss after six overs as Travis Head and David Warner flew out of the blocks with the Baggy Greens looking set for an easy victory.
But once Aiden Markram bowled Warner for 29, the wickets fell regularly with only Head (62) reaching his half-century as the five-time champions suffered a mid-innings wobble.
South Africa did not let any big partnerships bloom but Australia eventually reached the target with 16 balls to spare with Steve Smith (30) and Jos Inglis (28) providing useful cameos.
Captain Pat Cummins and Mitchell Starc saw their team over the line and they will now face India in Ahmedabad after the hosts defeated New Zealand in their last-four clash on Wednesday.
“It's hard to unpack all of that. I didn't move for the past couple of hours,” said player of the match Head, who also claimed two wickets in two balls to remove Heinrich Klaasen and Marco Jansen. “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. I think the pitches have been unbelievable. We knew it would be a grind and a battle and that's what it was.
“After the broken hand I thought I wasn't going to be here. I just want to contribute for Australia and will have another chance in a couple of days.”
Head's wicket of Klaasen (47 from 48 balls) was particularly important as he had begun to form a dangerous partnership with Miller. “I was under the pump and somehow that got through him,” said the part-time spinner. “I'm always keen to have a bowl.”
Earlier, Temba Bavuma's decision to bat under an overcast sky backfired and South Africa slumped to 24-4 inside 12 overs before light rain held up play.
Miller and Klaasen arrested the slide after play resumed with a 95-run partnership but Head's double strike put Australia back in charge.
A big six off Cummins brought up Miller his ton but he fell in the same over trying to clear the rope again. His 101 came off 116 balls, containing eight fours and five sixes.
Starc (3-34) and Cummins (3-51) finished with six wickets between them while Josh Hazlewood (2-12) and Head (3-34) claimed the rest.
“It's quite hard to put into words. Congratulations to Australia,” said Bavuma. “They were outstanding for a large part of the day.
“Our character came through. We showed the resilience we talk about and a bit of dogfight. 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.”