Captain Suryakumar Yadav top scored with 80, while Ishan Kishan blasted a quickfire 58 as India got the better of Australia off the last ball in the opening Twenty20 international of a five-match series on Thursday.
Rinku Singh blitzed a 14-ball 22 with four boundaries as India won by two wickets in Visakhapatnam.
Earlier, Josh Inglis hit his maiden international century to power Australia to 208-3.
Australia were invited to bat first in the match played just four days after their record-extending sixth ODI World Cup triumph in the final against hosts India.
The tourists lost an early wicket before Inglis, who smashed 110 off 50 balls, joined Steve Smith, who made 52 before being run out, to hammer 130 runs off 67 balls in a blistering partnership.
Inglis raised his fifty off 29 balls and completed his ton in 47 balls as he jumped and punched the air and the Australian dressing room stood up to applaud.
He finally fell to fast bowler Prasidh Krishna after his knock laced with 11 fours and eight sixes.
Australia, led by Matthew Wade, have rested many of their ODI stars — including Travis Head, Glenn Maxwell and Adam Zampa — as they plan for the T20 World Cup in June.