India claimed a consolatory 13-run win over Australia in the third and final one-day international in Canberra on Wednesday.

Australia wrapped up the series with comfortable back-to-back victories but saw their hopes of a 3-0 sweep dashed by an improved performance from India, who were boosted by batting first after Virat Kohli won the toss.

That allowed a sublime unbeaten partnership of 150 between Hardik Pandya and Ravindra Jadeja to lay down a marker, setting the hosts a target of 303.

Aaron Finch (75) and Glenn Maxwell (59) did not lack ambition in pursuit of that total, but India - led by Shardul Thakur (3-51) and Jasprit Bumrah (2-43) - protected their lead, bowling Australia out for 289 to get up and running ahead of the Twenty20 International series starting later in the week.

It had initially looked as though this could be another comfortable outing for Australia as wickets fell around Kohli and the captain was then stopped short on 63 following a successful review.

Kohli, who became the fastest man to 12,000 ODI runs on Wednesday, was caught behind off Josh Hazlewood, claiming the scalp of India's skipper for the third time in this series and the fourth time in his one-day career - a tally only bettered by four other bowlers.

It meant Kohli will finish a calendar year without an ODI century for the first time since 2008 - his debut year - but Pandya (92 not out) and Jadeja (66 no) picked up the slack.

They combined for 12 fours and four maximums to accelerate India to 302-5 and belatedly pose Australia a serious question.

David Warner had set the tone with the bat in the second ODI but missed out with injury here, meaning Marnus Labuschagne moved up to open and made only seven before playing onto his stumps from debutant T Natarajan - India's first powerplay wicket of the series.

Steve Smith, the outstanding centurion last time out, could only muster the same total, too, after sending Thakur through to KL Rahul.

Heavy lifting from Finch kept Australia on course, but attempts to maintain this momentum were disrupted by a further two telling Jadeja contributions.

Shikhar Dhawan caught at the second attempt at long-on as Finch tried to launch the all-rounder over the fence, before Jadeja stooped for a brilliant take himself off new boy Cameron Green (21).

Maxwell's big hitting - his four sixes including one that landed on the roof and another booming reverse sweep - took the result down to the wire, but his departure to a Bumrah yorker left Australia's tailenders with too much to do.