After being asked to bat first, India scored 295 for the loss of six wickets, thanks to Kohli for his brilliant 117 runs off 177 balls.
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John Hastings bagged a career-best four for 58 for Australia, who made life hard for themselves with the bat after Shaun Marsh’s 62, and the hosts had to rely on Maxwell’s 83-ball show-stealer.
The Indians were well in contention for their first win of the series when they had Australia in trouble at 215 for six.
The innings had started with Rohit at the crease fresh from two consecutive ODI hundreds, but this time he failed to reach double figures let alone triple. They had earlier conceded an away series in Bangladesh and went down to South Africa at home.
As in the earlier matches in this series, the visitors were let down by the bowlers despite putting up a big total.
India began to take hold of the game with the likes of Sharma, Jadeja and Yadav bowling in the right areas to deny the free-flow of runs to the Australian batsmen.
Australia once again threatened to make an easy chase of it, despite the seventh-over departure of Aaron Finch (21), caught behind off Umesh Yadav.
India have won only one of their last four series in the 50-over game. Jadeja had seen the back of its two chief tormentors, and there was more joy for India when Marsh nicked Ishant behind soon after, leaving Australia 167 for 4, with 129 to get from the last 20 overs and an undercooked middle-order exposed. They got a good score, to chase that down with James Faulkner in the end is unbelievable.
Ajinkya Rahane (50) also did well, scoring a half-century.
Kohli eventually popped up a Hastings delivery to George Bailey at cover, but skipper Mahendra Singh Dhoni came in and smashed 23 from nine balls to get India to their final score.
Virat Kohli delivered a decent knock of 59 runs from 67 balls, keeping things steady for the Indian team. He scooped a boundary over the head of wicketkeeper Wade off Hastings but next ball he again moved into position for a premeditated shot through the on side, and lost his leg stump, bowled for 68 off 91.
With 11 runs needed from 12 balls, Maxwell struck a six and a four before he was caught at mid-off in an attempt to complete his century.
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The Mumbai lad tried to pull Hastings for another six but could not clear the ropes.
