Turner then exploded down the order, clobbering six sixes and five fours in his charmed 43-ball blitz as Australia romped home with 13 balls to spare.
Earlier, Rohit Sharma (95) narrowly missed his century but Shikhar Dhawan roared back into form with a career-best 143 to help India post a commanding 358-9 after electing to bat first.
Dhawan went into the match having totalled 41 runs from his last five outings in limited-overs cricket, a run drought he ended with his 16th ODI hundred, raising 193 runs with fellow opener Rohit in the process.
Rohit clubbed a couple of sixes and seven boundaries to inch close to his century before his front-foot pull off Jhye Richardson found Handscomb at midwicket.
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Dhawan hit three sixes and 18 boundaries, stepping out even to the fast bowlers in a dominant display of batting. Pat Cummins ended the boundary carnage by bowling him out.
Rishabh Pant, replacing the rested Mahendra Singh Dhoni in one of the four changes to the India squad, made 36 before falling to Cummins (5-70) who claimed his maiden five-wicket haul in ODIs.
Australia, missing all-rounder Marcus Stoinis through a thumb injury, were jolted early in their chase.
Bhuvneshwar Kumar breached Aaron Finch's defence to dismiss the Australia captain for a duck in the first over and Jasprit Bumrah yorked Shaun Marsh in the fourth.
Khawaja and Handscomb defied India for nearly 30 overs and did not panic even as the required run rate climbed above nine.
Kuldeep Yadav denied Khawaja his second century of the series, dismissing the opener for 91.
Handscomb brought up his hundred off 92 balls to keep Australia on course, with the tourists needing 98 from the last 10 overs with six wickets in hand.
Yuzvendra Chahal eventually ended Handscomb's 105-ball knock, which included three sixes and eight fours.
Glenn Maxwell (23) could not provide the late assault but Turner tore into the Indian attack with some breathtaking power-hitting.
He needed 33 balls to bring up his maiden ODI fifty though was lucky to be dropped twice in three balls in the 47th over sent down by Kumar having also survived a stumping chance earlier in his knock.
The teams now move to New Delhi for the decisive fifth and final match of the series on Wednesday.
(Reporting by Amlan Chakraborty in New Delhil; editing by Clare Fallon)
