After restricting Australia to 160 for 6, Kohli (82 not out) provided the spark with a superlative display of batting to help India overhaul the target with five balls to spare in a thrilling showdown at the IS Bindra Stadium.
India turned the game on its head in the last four overs with the flamboyant Kohli unleashing a flurry of shots to take the game away from the Australians much to the delight of the capacity home crowd.
Captain Mahendra Singh Dhoni (18 not out) hit the winning runs — a four — to the wild celebration at the Indian camp as well among the vociferous crowd.
India, who finished second in Super 10 Group 2, will take on the West Indies in the second semifinals in Mumbai on March 31. New Zealand take on England in the first semifinals on March 30 in New Delhi.
Let down by a poor start, India were left to get 39 in the last three overs but Kohli got the team home to 162 for four in 19.1 overs. His 82 not out came from 51 balls, studded with nine fours and two sixes.
The 18th over bowled by James Faulkner went for 19 runs and that swung the game in the home team's favour.
The Indians lost openers Shikhar Dhawan (13) and Rohit Sharma (12), who both had not done much in the previous matches, early in the chase.
Dhawan top-edged a rising Josh Hazlewood delivery to short fine-leg before Rohit walked out of the crease to find his stumps disturbed off a slower ball by Shane Watson, leaving India at 37 for two in 5.5 overs.
All hopes were now pinned on premier batsman Kohli, who has made it habit of chasing down targets in testing times.
He started with a delectable flick and a square drive off Hazlewood, raising hopes of another successful chase through him. He stood strong as Suresh Raina (10) succumbed to the short-ball again, bringing in home hero Yuvraj Singh (21) at 49 for three.
The teams are
Rohit Sharma, Shikhar Dhawan, Virat Kohli, Suresh Raina, Yuvraj Singh, MS Dhoni, Hardik Pandya, Ravindra Jadeja, Ravichandran Ashwin, Ashish Nehra, Jasprit Bumrah
Aaron Finch, Usman Khawaja, David Warner, Steve Smith, Glen Maxwell, Shane Watson, James Faulkner, Peter Nevill, Adam Zampa, Nathan Coulter-Nile, Josh Hazlewood
Will India continue its dominance over Australia in T20s?
India and Australia face off in a crunch in the World T20 championship match in Mohali on Sunday which will be a virtual quarterfinals.
The winner enters the last four stage alongside New Zealand from Group 2.
In the last three meetings, India proved to be a stronger one in the shortest format of the game.
While India was unsuccessful in the ODI series Down Under in 2016, the Men in Blue won the T20 international series 3-0 and retained the No.1 spot in the rankings.
Source The Hindu