Electing to bat, the visitors piled up a mammoth 304 for eight relying on captain George Bailey's 85 and Aaron Finch's 72 and then shot India out for 232 in 49.4 overs to take 1-0 lead in the seven-match ODI series.
The Indian run chase under lights at the MCA Stadium never get going against the sustained and aggressive Australian bowling attack.
The visiting side, who were handed a four-wicket defeat in the one-off T20 International at Rajkot on October 10, bowled a disciplined line and length and choked the Indian batsmen in the middle overs.
Virat Kohli top-scored with 61 from 85 balls with six fours, while Suresh Raina contributed a 45-ball 39.
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Ravindra Jadeja (11) and skipper Mahendra Singh Dhoni (19) could not pull the team around after India slumped to 166 for five by the 35th over just before the power play and their dismissals in successive overs effectively ended the match.
For Australia, James Faulkner grabbed three wickets for while Clint McKay and Shane Watson chipped in with two wickets apiece. Mitchell Johnson, Aaron Finch and Adam Voges got a wicket each.
The two sides now moved to Jaipur for the second ODI on October 16.