Opener Nicole Bolton struck an unbeaten 100 off 101 balls after Australian spinners bamboozled the Indian batting to set up a crushing eight-wicket win in the opening game of the three-match series, which is part of the ICC Women's Championship.
Bolton's fourth ODI hundred ensured Australia reached a modest 201-run target in just 32.1 overs. The experienced Ellyse Perry (25 not out) hit the winning four.
India would have been bowled out for far less if it was not for the 76-run partnership between Sushma Verma (41) and Pooja Vastrakar (51) for the eighth wicket, helping them muster 200 in 50 overs.
Left-arm spinner Jess Jonassen led a stellar show from the Australian spinners, taking four wickets for 30 runs in 10 overs. Leggie Amanda-Jade Wellington picked up three wickets and Ashleigh Gardner removed Smriti Mandhana (12).
It was a sweet result for the visitors, who had lost to India in the World Cup semifinals. The second ODI will be played here on Thursday.
Australia were never in any sort of difficulty during the chase with Bolton anchoring the innings. Her sublime innings was laced with 12 fours. Bolton's opening partner Alyssa Healy made 38 and captain Meg Lanning 33 before being run out.
Electing to bat after winning the toss, India lost wickets at regular intervals before Vastrakar and Verma steadied the ship with sensible batting.
This was the 18-year-old Vastrakar's maiden half century, and she laced her crucial knock with seven boundaries and a six, while Verma found the fence three times during her 71-ball innings.
The total looked a far cry when Shikha Pandey was dismissed in the 32nd over with the score reading 113 for seven. That was the time when Verma and Vastrakar joined hands to bail India out of a precarious situation.
The hosts were off to a steady start with openers, Punam Raut (37) and Mandhana, putting on 38 runs in nine overs.
However, Mandhana was trapped in front of the wicket by Wellington in the first ball of the 10th over, giving the leg-spinner the first of her three wickets.
Debutant Jemimah Rodrigues (1) and Raut were also dismissed in quick succession as India were left struggling at 60 for three, which became 83 for four in the 23rd over. While facing 50 deliveries, Raut struck six boundaries and a six.
With skipper Harmanpreet Kaur (9) falling to Healy's work behind the stumps off Megan Schutt's bowling an over later, hosts India slumped to 87 for five.
The Australians were disciplined with the ball as spinners took eight wickets.