Australia won the third Twenty20 international by 12 runs in front of 30,000-plus fans at the Sydney Cricket Ground to prevent India from claiming a series sweep and ensure Virat Kohli's 85 came in vain.
Matthew Wade scored 80 from 53 balls and shared a 90-run fourth-wicket partnership with Glenn Maxwell (54 from 36) as Australia posted 186-5 after being sent in to bat.
Australia spinners Maxwell (1-20), Mitch Swepson (3-23) and Adam Zampa (1-21) combined for the first five Indian wickets before paceman AJ Tye removed Kohli, who had been dropped on one and 19, in the penultimate over to all but end India's chase.
India finished on 174-7 from their 20 overs as the series ended 2-1 to the tourists, who had been beaten 2-1 by Australia in the preceding one-day international series.
The sides will now contest four Test matches, beginning in Adelaide on December 17, before further games in Melbourne, Sydney and Brisbane.
Australia's innings in the final T20 was eventful, with Kohli denied a review for signalling too late on a not-out lbw decision against Wade.
The initial call would have been overturned if the challenge had been made within the required 15 seconds but Kohli's review came two seconds too late.
Wade told the on-field umpire that the replay was already being shown on the stadium screen when Kohli confirmed he wanted to refer the decision and the TV umpire agreed.
Maxwell was also dropped twice, saw off two DRS challenges after unsuccessful appeals from India to have him caught behind and was reprieved by a Yuzvendra Chahal no-ball.
The all-rounder had started walking off when he thought he was caught out - only to be called back when replays showed spinner Chahal had over-stepped.
Test hopeful Pucovski hurt after blow to head
Opening batsman Will Pucovski retired hurt in Australia A's tour match against India A after being hit on the helmet by a bouncer, raising doubts over his fitness ahead of the first Test against India.
Pucovski, who was struck by a delivery from Kartik Tyagi at Drummoyne Oval in Sydney, had been expected to partner Joe Burns at the top of the order in the opening Test with David Warner nursing a groin injury.
The 22-year-old, who has suffered a number of concussions in his career, will now sit out a second warm-up against India, which starts in Sydney on Friday.
John Orchard, Cricket Australia's chief medical officer, said: "Will experienced mild concussion symptoms but was able to leave the field unassisted. He was monitored in our medical room and was communicating freely with staff and teammates as well as family over the phone."