Having set India 161 to win in Mohali, Australia had its noses in front heading into the final five overs, with MS Dhoni’s side still needing 59 runs with six wickets in hand.
But Kohli put the foot on the gas from three, racing from 37 off 32 to 82 off 51 to guide India to victory.
In a 67-run partnership with Dhoni, Kohli scored 47 runs, hitting seven boundaries and one six in the last five overs.
James Faulkner and Nathan Coulter-Nile were particularly targeted by Kohli. Faulkner was hit for two fours and a six off his three balls in the 18th over, while Coulter-Nile leaked four boundaries in the penultimate over.