George Bailey had enhanced his Ashes credentials with 156 while Shane Watson struck 102 from 94 balls as Australia set the hosts a massive 351 to win.
But India set about their task with typical flamboyance, Shikhar Dhawan scoring his third ODI century from 102 balls, amid an opening partnership with Rohit Sharma (79) of 178 before Kohli (116 not out) put on an unbeaten 61 for the fifth wicket with captain MS Dhoni to spark scenes of jubilation with three balls to spare.
Victory sets up a series decider between India and Australia on Saturday, with the seven-match series square at 2-2.
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