The Indians, chasing their first victory on their tour of Australia, rocked the home side with brilliant ground fielding led by two run outs from Ravindra Jadeja.
Opener Aaron Finch, one of three changes from Australia's 31-run win in Wednesday's opening T20 game, topscored with 36 off 23 balls and first match topscorer Matthew Wade chipped in with 32 off 29 balls.
But India had the home side under pressure from the third over when they had T20 specialist David Warner dismissed for eight to a great catch in the deep by a back-pedalling Gautam Gambhir off Praveen Kumar.
Test flop Shaun Marsh was out for a two-ball duck and Finch was run out by an outstanding piece of athletic fielding by Jadeja after David Hussey hit straight to him at backward point and scampered for a single.
Hussey also played a role in a second run out as Jadeja found skipper George Bailey (3) well out of his ground at the bowler's end, and was himself next to go, caught and bowled by Jadeja for 24 off 29 balls.
Smart glovework by skipper M.S. Dhoni had Mitchell Marsh stumped for 13 off spinner Rahul Sharma and Wade was run out by a direct throw from Rohit Sharma in the 19th over.
The Australians collapsed losing their final three wickets in seven balls.
Clint McKay was caught by Dhoni off Vinay Kumar for a first-ball duck, veteran Brad Hogg was leg before wicket to Rahul Sharma for four and Xavier Doherty was run out by Suresh Raina attempting a suicidal second run to end Australia's innings with two balls left.
Kumar took two for 21 off three overs and Sharma claimed two for 29 off 3.4 overs.
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