Travis Head starred with bat and ball as Australia set up a "special" World Cup final clash with India after a tense three-wicket win over South Africa in Kolkata on Thursday.

Chasing a tricky 213 for victory, Australia wobbled after Head hit 62 but Steve Smith (30) and Josh Inglis (28) helped the five-time champions reach their target with 16 balls to spare in the second semi-final in Kolkata.

"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," said Head.

As Australia reached an eighth World Cup final, South Africa were left to rue a fifth semi-final loss despite David Miller's 101.

It was particularly painful for the Proteas who had routed Australia by 134 runs in a group stage game at Lucknow four weeks ago.

Australia slipped to 137-5 and then 193-7 before Mitchell Starc (16) and skipper Pat Cummins (14) kept their nerve to steer the team home.

"It's going to be a special final, I still talk of the 2015 as one of my career highlights and I wasn't even playing," said Cummins of the final in Melbourne eight years ago when Australia defeated New Zealand.

"So to be out there in a final, in India, world's biggest stadium...it's a very happy changing room at the moment."

The final is on Sunday at the world's biggest cricket stadium in Ahmedabad which boasts a 130,000-capacity.

Two-time champions India made the final on Wednesday with a 70-run victory over New Zealand in Mumbai, taking their record at this World Cup to 10 wins in 10 games.

Left-handed batsman and part-time off-spinner Head stood out after taking two wickets and then with his 48-ball innings laced with nine fours and two sixes.

Australia were in trouble when they were five down as spinners Keshav Maharaj and Tabraiz Shamsi struck in quick succession to rattle the middle-order.

Maharaj bowled Head, who was dropped on 40 and 57, and Shamsi, a left-arm wrist spinner, trapped Marnus Labuschagne lbw for 18 and bowled Glenn Maxwell for one in his next over.

Australia started the tournament with two losses but registered their eighth straight win.

"The way we started with the bat and ball was the turning point, we always had to play catch-up," said South Africa skipper Temba Bavuma.

'Ruthless Australia'

"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."

Starc led the bowling charge with figures of 3-34 and Cummins also picked three wickets to bowl out South Africa for 212 in 49.4 overs.

Left-arm quick Starc struck in the first over to send back Bavuma, who had said he was not "100% fit" at the toss, for a fourth-ball duck.

Josh Hazlewood claimed the wicket of in-form Quinton de Kock for three as Cummins took a stunning catch.

De Kock, who will quit one-day international after the World Cup, ended with 594 runs including four centuries to sit behind the tournament's leading batsman Virat Kohli (711).

The new-ball bowlers kept up the attack with the wickets of Aiden Markram (10) and Rassie van der Dussen (six) as South Africa slumped to 24-4 and were 44-4 when rain interrupted play.

Klaasen and Miller hit back after the 45-minute rain break as the two put on 95 runs but Head broke through to bowl Klaasen for 47.

Head trapped Marco Jansen lbw on the next delivery to be on a hat-trick, which was saved by Gerald Coetzee, who put on a 53-run partnership with Miller.

The left-handed Miller smashed eight fours and five sixes in his 116-ball knock.

AFP