Aaron Finch (72 off 79 balls) and captain George Bailey (85 off 82) set up Australia's 304 for eight before their bowlers did a brilliant job to stop India at 232 all out in 49.4 overs. James Faulkner struck thrice while other pacers Shane Watson and Clint Mckay picked up two wickets each.
It was a good comeback from the visitors who were outplayed in the one-off T20 Thursday. The second ODI takes place in Jaipur Wednesday.
Australian bowlers learnt their lessons from the Rajkot tie and bowled a much better length, using the odd short and slower ball to good effect.
The stylish opening pair of Shikhar Dhawan (7) and Rohit Sharma (42) found it tough to push the scoring rate.
Faulkner had Dhawan caught behind with an away going ball. The left-arm pacer's celebrations went awry as he ended up hitting wicketkeeper Brad Haddin in the eye while going for a high-five.
After the opener's departure, Virat Kohli (61 off 85) and Suresh Raina (39 off 45) too did not get many loose deliveries from the opposition attack. They put up 71 runs together but were not able to find the boundaries needed to keep up with the asking rate.
Their fall along with the in-form Yuvraj Singh (7) meant Indian were struggling at 166 for five in the 35th over, needing another 139 off 92 balls.
It was time for another Mahendra Singh Dhoni special but when the Indian captain was bowled by Mckay, the target seemed out of reach for the hosts. The ball did just enough to disturb his off-stump.
Australia, just like the India innings, made a cautious start on a pitch assisting the fast bowlers.
Openers Phil Hughes (47 off 53) and Finch went for their strokes after getting their eye in.
Finch as expected was the aggressor in the 110-run stand, smashing the spinners and pacers alike.
Ravindra Jadeja made the much needed breakthrough by removing Hughes. Yuvraj had the dangerous Watson (2) caught at long on in the next over, making it 113 for two in the 19th over. Watson played a bad shot and lofted it straight into Jadeja's hands, gifting Yuvraj his first ODI wicket since the 2011 World Cup.
His second scalp was Finch, who hit straight to Kohli at long off ending an innings that included three cracking sixes and eight boundaries. His back brought relief to the Indian camp as the Victoria born cricketer looked in ominous touch and had made a blistering 89 in the one off T20 in Rajkot.
Yuvraj then showed again that he was back to full fitness, getting Adam Voges run out with a spectacular direct hit, leaving the Aussies 172 for four with 18 overs to spare.
Bailey played a captain's knock to take his team to a competitive total and was aided by a timely cameo from Glen Maxwell (31 off 23).