After amassing 334-5 from their 50 overs, Australia restricted India to 313-8 at the M Chinnaswamy Stadium in Bengaluru to narrow the host's lead in the five-match series to 3-1. The result denied India from securing a 10th straight ODI win.
India's openers got them past the 100-run mark before Ajinkya Rahane (53) fell to Kane Richardson. His partner Rohit Sharma was run out shortly after for 65 following a mix-up with skipper Virat Kohli.
Kedar Jadhav (67) and Hardik Pandya (41) led a spirited fightback with a 78-run fourth-wicket stand after Kohli's dismissal. Jadhav fell after a 61-run partnership with Manish Pandey as Australia's bowlers held their nerve to seal the win.
Nathan Coulter-Nile claimed two wickets while fellow paceman Richardson picked up three.
Earlier, Warner and Finch took the attack to the Indian bowlers to eclipse Australia's previous best opening stand against India which was the 212 set by Geoff Marsh and David Boon in Jaipur in 1986.
Warner smashed 12 boundaries and four sixes as he became the eighth batsman to score a ton in his 100th match, reaching the milestone in the 31st over.
He was particularly severe against the spinners, but when he looked to shift gears, he was caught trying to loft Jadhav out of the park from the final ball of the 35th over.
Finch, a century-maker in the previous match at Indore, missed the chance of another, offering a simple catch to Pandya at mid-on off paceman Umesh Yadav five balls later.
Australia, whose previous ODI victory was over Pakistan in Adelaide on January 26, will look to end the series with another positive result when the teams meet in Nagpur on October 1.
