Australian spinners Adam Zampa and Ashton Agar turned the match to hand India their first one-day international series defeat at home since 2019 in a thrilling third and final match in Chennai on Wednesday.
Left-arm spinner Agar removed in-form Virat Kohli (54) and the world's top-rated Twenty20 batter Suryakumar Yadav for his third consecutive golden duck with the first two balls of the 36th over to leave the hosts reeling at 185-6 with a target of 270 to win.
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The visitors won the match by 21 runs after bowling out the hosts for 248 in the last over.
The 2-1 win in the series was also important practice on South Asian pitches for Australia before the ODI World Cup in India later this year.
Australia's stand-in-captain Steve Smith won the toss and chose to bat first in the series-decider.
India bowled out Australia for 269 and were cruising in the first 10 overs of their chase before skipper Rohit Sharma fell after a 17-ball 30 with the team at 65-1.
Sharma's in-form opening partner Shubman Gill fell after a steady 49-ball 37 to leg-spinner Zampa.
India's star batters Kohli and KL Rahul struck a busy 69-run partnership before Rahul fell to Zampa for 32.
The hosts' otherwise reliable lower-middle order offered little resistance. All-rounders Hardik Pandya (40) and Ravindra Jadeja (18) also fell to Zampa, who finished with 4-45 in his 10-over spell.
Zampa was named player of the match but said his spin-partner Agar, who finished with 2-41, actually "changed the game".
"I probably don't think I deserve this one tonight to be honest," Zampa said after the game.
"Kudos to the guys who bowled before me as well.... We always have a lot of trust in each other, trust in our process and trust in our game plan. and we stick to it," he added.
Australian pacers Sean Abbott and Marcus Stoinis took one wicket each.
Three wickets apiece from Hardik Pandya and Kuldeep Yadav left India in need of 270 to win the series, which stood at 1-1 going into the final game.
Sharma said that Indian batters failed to carry on after getting a start to "take the game deep".
"All of us were trying our best to go out and achieve that but it just didn't happen," the Indian skipper said.
"Obviously a loss like this really hurts. But again we can understand what we need to do better as a team, as a group," he added.
Earlier, Pandya (3-44) and India's left-arm spinner Kuldeep (3-56) played an important role in restricting Australia to a chaseable 269 in the 49th over.
By the eighth over, in-form openers Travis Head and Mitchell Marsh had hit 10 boundaries between them, including three sixes, and looked set for a commanding partnership before Pandya took the quick wickets of Head (33), Smith (0) and Marsh (47).
Yadav had the better of the middle order beginning with David Warner, who made 23 batting at number four on his return from the elbow fracture that forced him out of the second Test in February.
Marnus Labuschagne (28) was next but Alex Carey stubbornly held on for another 10 overs before his departure on 38.
Left-arm spinner Axar Patel and frontline pacer Mohammed Siraj each took two wickets as Sean Abbott (26), Agar (17) and Mitchell Starc (10) added important runs to a below-par score.