Australia allrounder Marcus Stoinis took two wickets in the last over Wednesday as India's batting lineup collapsed late to lose its tour-opening Twenty20 international by four runs.
Virat Kohli returned to lead India after skipping the last series against West Indies and, after winning the toss and sending Australia in to bat, had a below-par night, dropping a regulation catch in the fourth over, misfielding later in the innings and getting out for four.
The Australians posted 158-4 in a rain-interrupted 17 overs with Glenn Maxwell (46 from 24 balls) and Chris Lynn (37 from 20 balls) each belting four sixes.
The rain delay brought the Duckworth-Lewis rules into play, and India had a revised target of 174 from 17 overs.
Shikhar Dhawan set India up in its run chase with a 42-ball 76 that included 10 boundaries and two sixes before he upper cut a short ball from Billy Stanlake to Jason Behrendorff on the third man boundary and India slipped to 105-4 from 11.4 overs.
He raised his 50 with a six over backward square, his first, and had a reprieve on 65 when Adam Zampa put down a return catch, but finally succumbed to the short-pitch tactic.
His wicket came in a spell when India lost 3-24, and seemed to give Australia the advantage. But Rishabh Pant (20) and Dinesh Karthik (30) took up the attack and plundered 25 from one over by Andrew Tye after a tactical blunder by Australia captain Aaron Finch, who lost track of the new bowling restrictions.
The pair put on 51 for the fifth wicket to give India the ascendancy before Pant paddled an easy catch to Behrendorff off Tye's bowling to again change the momentum, leaving India needing 18 runs from nine balls.
Stoinis bowled the last over, with India needing 13 runs and took pace off the ball and picked up the wickets of Krunal Pandya and Khartik caught in the outfield as India finished 169-7.
India has won its last seven T20 series, and Kohli's squad is using the three-game series in the shortest format to fine-tune for the bigger prize starting next month when it chases its first ever test series victory in Australia.
Australian cricket has been in turmoil since a ball-tampering scandal in South Africa in March and is coming off back-to-back series losses to Pakistan in the United Arab Emirates and at home against South Africa.
On top of that, the hosts were missing frontline bowlers Mitchell Starc, Pat Cummins, Josh Hazlewood and offspinner Nathan Lyon, who were preparing for the four-match test series which kicks off December 6 in Adelaide.