Opener Usman Khawaja's maiden one-day international century backed up by decent bowling performance helped Australia outplay India by 32 runs to stay alive in the five-match series on Friday.
Adam Zampa led the bowling with three wickets including the all-important scalp of India captain Virat Kohli, for 123, to help dismiss the hosts for 281 in 48.2 overs while chasing 314 in Ranchi.
Fast bowlers Pat Cummins and Jhye Richardson also took three wickets each and combined to wipe off the Indian tail after Kohli's second successive ton gave the tourists a scare.
Kohli, who struck a match-winning 116 in the second ODI, smashed 16 fours and a six during his 95-ball knock before being bowled off Zampa's leg-spin googly.
For Australia, Khawaja, who made 104, and skipper Aaron Finch, who hit 93, put on a 193-run opening stand to guide their team to 313 for five after being put in to bat.
"It was a pretty good performance. To get 300 on that wicket was very good. It was nice and especially in these conditions," Finch said after the win.
"I have been working really hard and have always had the faith I would get runs. Usman played a fantastic knock, Jhye was also impressive with the ball," he added.
Finch, whose last significant one-day score was a 100 in England in June 2018, struck form with his 19th ODI 50 but fell short of his century after being trapped lbw off Kuldeep Yadav.
The left-handed Khawaja, who hit 11 fours and a six in his 113-ball knock, kept up the pace during a 46-run second-wicket stand with the in-form Glenn Maxwell, who made 47.
Khawaja fell to paceman Mohammed Shami and Maxwell, who smashed three fours and three sixes in his 31-ball blitz, was run out by wicketkeeper Mahendra Singh Dhoni.
Yadav soon halted Australia's surge with his left-arm wrist spin as he sent back Shaun Marsh, for seven, and Peter Handscomb, for nought, in the space of three deliveries.
But Marcus Stoinis, on 31, and Alex Carey, on 21, put on an unbeaten 50-run stand to take Australia well past the 300-run mark.
Kohli tried to set up India's chase after they were in trouble at 86 for four following the departure of Dhoni for 26.
The 30-year-old Kohli, who registered 41st ODI ton, built crucial partnerships including an 88-run fifth-wicket stand with Kedar Jadhav to challenge the opposition attack.
Vijay Shankar also made a useful 32 but the ever-increasing run rate got to the Indian chase.
The fourth ODI is on Sunday in Chandigarh.