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India lead the three-match series 1-0.
Chasing a target of 189, India were 16/3 and subsequently 39/4 but Rahul held his nerves during a 91-ball knock that had seven fours and a six. He added 108 for the unbroken sixth wicket stand alongside Ravindra Jadeja (45 not out).
Earlier, India bowled out Australia for 188.
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Opening in place of the injured David Warner, Mitchell Marsh top-scored for Australia with a 65-ball 81, but the rest, including skipper Steve Smith, failed to make any worthwhile contribution.
Brief scores:
Australia: 188 all out in 35.4 overs (Mitchell Marsh 81; Mohammed Shami 3/17, Mohammed Siraj 3/29).
India: 191/5 in 39.5 overs (KL Rahul 75 not out, Ravindra Jadeja 45 not out, Mitchell Starc 3/49).