Rohit Sharma's century went in vain as Australia chased down India's 267 for eight to reach the target of 269 runs by losing six wickets in 49 overs.
India had created some chances by picking up three quick wickets of Steve Smith (47), Finch and George Bailey (5) in a gap of 23 balls. But it was wicket-keeper Brad Haddin (13*) and
James Faulkner (9*) who reached the target and helped the home side their second consecutive victory in the tournament.
Australian opener Warner (24) and Finch had provided Australia the much needed start to the match by posting 51 runs in the opening wicket partnership.
After Warner departed, it as seasoned Shane Watson who added 41 runs while Smith contributed 47 runs with their willows.
Glenn Maxwell (20) failed to contribute with his willow in the match.
Umesh Yadav prevented Finch from scoring a century and stopped him at 96.
Yadav picked up two wickets for India.
Earlier, riding on Rohit Sharma's 138 runs innings, which included nine boundaries and four sixes, India had posted 267 runs for the loss of eight wickets.
Shikhar Dhawan failed with his willow and contributed only 2 runs while Suresh Raina contributed 51 runs with his willow.
Other Indian batsmen like Ajinkya Rahane (12), Virat Kohli (9) and MS Dhoni (19) did not click with their bats for India in the match.
Starc took six wickets by giving away 43 runs in his 10 overs by Australia.
India will now face England on Tuesday.
The series assumes significance for all the three teams as they are all gearing up for the World Cup to be held in Australia and New Zealand from next month.
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