Set 231 to win Friday's decider, India chased their target with four balls to spare to claim a 2-1 series victory and cap off a summer of unprecedented triumph.
Superstar veteran Dhoni again steered India to victory, scoring an unbeaten 87 off 114 balls - his third fifty from as many games - to repeat his match-winning heroics in Adelaide.
In a gripping finish, Dhoni was dropped on 74 by Aaron Finch at mid-off, then partner Kedar Jadhav (61 not out) barely survived a run-out attempt at the non- striker's end.
Jadhav then scored the winning runs to the jubilation of a crowd of 53,603 dominated by Indian fans who chanted Dhoni's name.
"It's been an amazing tour," skipper Virat Kohli said.
"We drew the T20 series, won the Test series and now the ODIs. If you had given me these results before the tour, I would have gladly taken it."
It is Australia's seventh straight ODI series defeat, extending a two-year winless streak that has alarm bells ringing for the team's World Cup title defence.
Dhoni and Kohli (46) were both able to capitalise on Australia's poor fielding and questionable use of the Decision Review System (DRS).
Dhoni survived being out for a golden duck to Marcus Stoinis when Glenn Maxwell dropped a straightforward chance at point, while replays showed Finch should have reviewed a caught-behind opportunity when Dhoni was on 34.
Kohli was dropped by Peter Handscomb at second slip on 10 and survived a run-out opportunity on 32.
"We took it down to the wire but when you give great players a couple of chances, it's always tough," Australian skipper Finch said.
"The boys gave it everything."
Much of the post-mortem is bound to focus on Australia's batting.
Openers Finch and Alex Carey again failed to produce runs while Shaun Marsh (39), Usman Khawaja (34) and Maxwell (26) were unable to build on promising starts, forcing Handscomb (58) to fight a lone hand with the tail.
Legspinner Yuzvendra Chahal led the way for India, celebrating his ODI recall at the expense of mystery spinner Kuldeep Yadav with career-best figures of 6-42.
Sensing opportunity in overcast conditions which caused a brief rain delay, Kohli reaped immediate rewards after winning the toss and opting to bowl first.
Both Carey and Finch fell cheaply to swing king Bhuvneshwar Kumar, the latter trapped lbw on 14 to cap off a miserable summer across all three formats.
Chahal then struck twice in his first over to remove the in-form Marsh and Khawaja, who had combined for a 73-run partnership.
Maxwell came to the crease in the 30th over - the earliest Australia's No.7 had been required for the series - but soon fell to Mohammed Shami, squeezing an ill-judged pull shot to a brilliantly diving Bhuvneshwar at deep fine leg.