Australia won the toss and chose to field first.
India scored 188/3 in their given 20 overs as Kohli was the top scorer for the visitors. He made 90 runs from 71 balls with the help of nine fours and two sixes.
Suresh Raina and Rohit Sharma scored 41 and 31 runs respectively.
Shane Watson took two wickets for Australia whereas James Faulkner dismissed one batsman.
The Australian side, chasing 189 runs to win, were bowled out on 151 in 19.3 overs.
Skipper Aaron Finch made 44 runs while Steve Smith and David Warner scored 21 and 17 runs respectively.
Debutante Jasprit Bumrah took three wickets while Ravi Ashwin, Ravindra Jadeja and Hardik Pandya dismissed two batsmen each.