Veteran wicketkeeper Mahendra Singh Dhoni expertly guided India to the win with an unbeaten 87 with solid support from Kedar Jadhav on 61 not out.
India made three changes to their team with Mohammed Siraj making way for ODI debutant Vijay Shankar, wrist-spinner Yuzvendra Chahal for Kuldeep Yadav and all-rounder Kedar Jadhav for Ambati Rayudu.
Earlier after winning the toss, Team India invited Aaron Finch-led Australia to bat first.
For the tourists, Chahal was helped by the opening pair of Bhuvneshwar Kumar (2/28 off eight overs) and Mohammed Shami (2/47 off 9.4 overs). There were two incidents of confusion between the wickets first in the 21st over when Kohli was stranded and was saved for a lack of a direct hit.
From a dasher, to a finisher to finally the anchor in the last leg of his career, Dhoni 3.0 was in full flow during India's successful chase of 231 on a sluggish Melbourne pitch after Yuzvendra Chahal set it up with a career-best 6 for 42.
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Meanwhile, the hosts have made two changes to their playing XI on the eve of the decider.
Billy Stanlake replaces Jason Behrendorff, who is suffering from a back injury.
"He's been monitored. Just a bit of a sore back. he's had some back issues in the past so I think it's about managing him through this series and further forward", captain Aaron Finch said before training on Thursday.
"Jhye has had an impressive first half in his Sheffield Shield season and no-one could deny he has now continued that form in ODI matches for Australia", said national selector Trevor Hohns. Pacer Kane Richardson has also been called into the squad as a cover.
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.