India had lost the first two ODIs in Sydney to hand Australia a decisive 2-0 lead in the series.
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Electing to bat, India scored 302 for five with Hardik Pandya (92 not out) and Ravindra Jadeja (66 not out) rasing an unbeaten 150-run stand for the sixth wicket.
In reply, Australia managed 289 in 49.3 overs.
Brief Scores:
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Australia: 289 all out in 49.3 overs (Aaron Finch 75, Glenn Maxwell 59; Shardul Thakur 3/51, Jasprit Bumrah 2/43)