Chasing 287 to win, India overhauled the target with 15 balls to spare at M Chinnaswamy stadium.
Young batsman Shreyas Iyer, who scored unbeaten 44, completed the win in company of Manish Pandey (8).
Earlier, Steve Smith (131) hit a hundred to lead Australia to 286 for nine.
Apart from Smith, who raised his ninth ODI hundred, young Marnus Labuschagne (54) also batted well after the visitors opted to bat.
Down the order, Alex Carey contributed 35 runs though he could not make the most of his start.
For India, pacer Mohammed Shami (4/63) and spin all-rounder Ravindra Jadeja (2/44) shared six wickets between them.
India had lost the series-opener in Mumbai before levelling the series in Rajkot.
Australia: 286 for 7 in 50 overs.(S Smith 131, M Labuschagne 54; M Shami 4/63, R Jadeja 2/44).
India: 289 for 3 in 47.3 overs. (R Sharma 119, V Kohli 89; A Agar 1/38, A Zampa 1/44).