Rohit Sharma and Shikhar Dhawan hit a first-wicket partnership of 40 runs before the former was taken out for 31 off 20 balls by Shane Watson in Adelaide.
Virat Kohli was the star for India as he reached the end of 20 overs with an unbeaten knock of 90, while Suresh Raina contributed with 41 runs before he was bowled out by James Faulkner.
The tourists ended the innings on 188-3, giving Australia a reachable target, but the hosts’ batting order collapsed following the dismissal of David Warner, who managed just 17 runs.
Aaron Finch top-scored with 44 off 33 balls, but it was India’s spinners who dominated as Australia fell from 89-1 to 151 all out.
Jasprit Bumrah took three wickets, while Ravichandran Ashwin, Ravindra Jadeja and Hardik Pandya took two apiece, and Ashish Nehra claimed one.
By Taiwo Oyedeji
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