Australia will play Virat Kohli and India for the Cricket World Cup trophy after beating South Africa by three wickets in a semi-final thriller on Thursday.

After restricting the South Africans to 212, Australia eked their way to 215-7 to win with 16 balls to spare in a tense atmosphere inside Eden Gardens.

Australia will be bidding to win the 50-over World Cup for a record-extending sixth time, while host nation India are seeking a third title.

The championship match is in Ahmedabad on Sunday.

South Africa have never won a semi-final match at the World Cup in five attempts.

Australia have only lost once in nine World Cup semifinals. Reaching the final at this edition marked a stunning turnaround for the five-time champions after losing their first two matches in the group stage.

They went on to lift the trophy after beating South Africa in both 1999 and 2007 but face a formidable test on Sunday against India, who have won 10 matches at this edition.

Travis Head scored 62 off 48 balls to give Australia's chase a fast start. South Africa refused to give up and reduced Australia to 137-5 in the 24th over with the valuable wicket of Glenn Maxwell for just 1.

Steve Smith registered a cautious 30 runs off 62 balls before he was dismissed to make it 174-6 in the 34th over.

Australia kept their nerve and crossed the finish line in the 48th over.

Mitchell Starc’s 16 not out off 38 balls and skipper Pat Cummins's 14 off 29 saw their team into the final for a record eighth time. (AP)