With this win, India entered the final awaiting the opponent based on the winner from the other semi-final between New Zealand and South Africa.
The Rohit Sharma-led side chased a target of 265 runs in 48.1 overs.
Besides Kohli, Shreyas Iyer (45), KL Rahul (42 not out) and Hardik Pandya (28) also played crucial roles in India's success.
Earlier, a disciplined bowling team helped India restrict Australia for 264.
After winning the toss, Australia opted to bat first.
Mohammed Shami was the pick of Indian bowlers with figures of 3 for 48 while Varun Chakravarthy and Ravindra Jadeja picked two apiece.
For the Australian side, Steve Smith was the top-scorer with 73 runs off 96 balls.
India are set to take on the winner of the South Africa vs New Zealand match in the final on Sunday.