The Australians posted 158-4 in a rain-interrupted 17 overs with Maxwell (46 from 24 balls) and Chris Lynn (37 from 20 balls) each belting four sixes and Stoinis finishing unbeaten on 33.
The rain delay brought the Duckworth-Lewis rules into play, giving India 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, including one over backward square to raise his half century.
He had a reprieve on 65 when Adam Zampa put down a return catch, but was finally out upper cutting a short ball from Billy Stanlake to Jason Behrendorff on the third man boundary as India slipped to 105-4 in the 12th over.
His wicket came in a period 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 swing 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 as he picked up the wickets of Krunal Pandya and Karthik before India finished 169-7.
Kohli described it as a "sort of see-saw battle" and Dhawan said the India squad wasn't overly disappointed with the narrow loss.
A missed runout when Maxwell was on 9 and a few dropped catches were momentary setbacks for India, Dhawan said, but "we got a lot of confidence out of this game and we're going to take it forward for the next game."
Stoinis said he enjoyed the pressure of bowling the last over and hoped Australia was turning a corner after losing four consecutive T20s.
"We've got good memories in the team," he said. "We dominated T20s last year. We were No. 1 or 2 in the world rankings not long ago. We're confident."
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, Australia was missing frontline bowlers Mitchell Starc, Pat Cummins, Josh Hazlewood and Nathan Lyon, who were preparing for the four-match test series which kicks off Dec. 6 in Adelaide.
- news.com.au/AP
