Man-of-the-series in India's 4-1 defeat in the one-day internationals, Rohit hit a 47-ball 60 at the top of the order to give the touring side a fast start along with partner Shikhar Dhawan (42).
India, who were put in to bat, rode an opening stand of 97 to reach 184-3 in their 20 overs with Kohli providing a late assault in a strong top-order performance with a swashbuckling unbeaten knock of 59.
Kohli, who smashed an unbeaten 90 in India's 37-run win in Adelaide on Tuesday, hit seven boundaries and a six during his 33-ball knock.
Australia, who made six changes in the side from their last defeat, also made a strong start with captain Aaron Finch providing the fireworks.
News that makes sense
Your trusted source for staying up-to-date with the world around you. Get free daily news updates and analysis, straight to your inbox.
Finch (74) and Shaun Marsh added 94 for the opening wicket to keep Australia, who handed T20 debuts to three players, in the hunt but India's spinners picked up quick wickets to halt their march.
Finch hit eight fours and two sixes in his 48-ball knock before he was run out trying to steal a quick single.
India captain Mahendra Singh Dhoni missed a regulation stumping off Marsh but made amends with smart work with the gloves to dismiss dangerman Glenn Maxwell for one off left-arm spinner Yuvraj Singh.
Dhoni was also lucky when the ball ricocheted off his pads to hit the stumps with James Faulkner out of his crease, the dismissal snuffing out Australia's hopes of levelling the series at 1-1.
The hosts could only manage 157-8 in their 20 overs. Left-arm spinner Ravindra Jadeja and Jasprit Bumrah picked up two wickets each for India.
The final match of the series will be played in Sydney on Sunday.
(Reporting by Sudipto Ganguly in Mumbai; editing by Ed Osmond)
