Manish Pandey's maiden ODI ton ruined Australia's hopes of whitewashing India as the tourists secured a nervy six-wicket triumph in the final match in Sydney.
Pandey biffed 104 not out from 81 balls, sharing vital partnerships of 97 with Rohit Sharma (99) and 94 with captain MS Dhoni (34) as India chased down their hosts' total of 330-7 with two balls to spare to reduce their arrears in the series to 4-1.
Australia's Mitchell Marsh (102no from 84) had earlier notched his first ODI hundred, with David Warner (122 from 113) blasting his fifth, but those knocks were not enough for the hosts, who saw their 18-match ODI winning streak on home soil halted.
Warner, who lost opening partner Aaron Finch (six) in the first over, put on 58 with captain Steve Smith (28) for the second wicket, though Australia were pegged back to 117-4 when Smith fell to debutant Jasprit Bumrah, and George Bailey (six) and Shaun Marsh (seven) were dismissed cheaply.
However, Warner and Marsh shared a fifth-wicket stand of 118 - taking particular liking to Umesh Yadav (1-82 from eight overs) - before Marsh and Matthew Wade (36 from 27) lifted Australia above 300 with a swashbuckling partnership of 85 in 8.4 overs.
Marsh, whose previous best ODI score was an 89 against Zimbabwe in 2014, secured his century in the final over, with 22-year-old paceman Bumrah, who also clean bowled James Faulkner (one) with a rip-snorting yorker, the pick of India's attack with 2-40.
Bumrah and Ishant Sharma (2-60) ensured Australia procured just seven runs from the final two overs and the tourists carried that momentum into their knock, with Shikhar Dhawan (78 from 56) and Rohit Sharma adding 123 in 18.2 overs up top.
John Hastings (3-61) then removed Dhawan and Virat Kohli (eight) in quick succession, Dhawan caught brilliantly by Shaun Marsh at deep point and Kohli - whose first-ball four was chalked off after deflecting off Spidercam - nicking off moments after reaching 1,000 ODI runs against Australia.
Sharma and Pandey combined to add 97 before Sharma, dropped on 51 by Smith and on 88 by Shaun Marsh, snicked Hastings behind, the right-hander's frustration at missing out on three figures perhaps mildly tempered by him becoming the 12th Indian batsman to surpass 5,000 ODI runs.
Dhoni was happy to let Pandey, who scored 71 on ODI debut against Zimbabwe, dominate the pair's partnership but with India needing 13 from the final over, he cut loose, creaming Mitchell Marsh down the ground for six.
The captain perished from the next delivery, leaving Pandey to steer for four through third man to bring up his century, off 80 balls, and then launch over cover for the match-winning two as Australia lost their first ODI at home since being beaten by South Africa in Perth in November 2014.
Australia and India will now meet in three T20Is, with matches scheduled in Adelaide on Tuesday (8.35am, Sky Sports 1), Melbourne on Friday (8.35am, Sky Sports 1) and Sydney on Sunday, January 31 (8.15am, Sky Sports 2).