The seven-match series is now tied at 1-1 following the Aussies' 72-run victory in Pune last weekend.
The tourists won the toss and chose to bat first before going on to make a score of 359-9 from their 50 overs.
However, an unbeaten 141 from Rohit Sharma helped India get to 362-1 with 39 balls remaining.
Meanwhile, Finch and Maxwell were both run out by the quick Indian outfield.
Despite being given a big target to chase, India's top order were in dominant form with the bat and made light work of Australia's bowlers.
Sharma smashed his 141 off 123 balls, while Shikhar Dhawan made 95 before he was dismissed by James Faulkner.
Meanwhile, Virat Kohli scored the fastest ODI century by an Indian as he reached the landmark off 52 balls.