Glenn Maxwell struck a crucial half-century as Australia edged out India by three wickets in a thrilling last-ball finish in the first of three T20 internationals.
Pat Cummins hit a four and took two runs to complete a nervous 127-run chase after his fellow paceman Nathan Coulter-Nile took three wickets to restrict India to 126-7.
Maxwell, who made 56, put together 84 runs with D'Arcy Short for the third wicket to put Australia on track before Jasprit Bumrah struck with three wickets.
Bumrah got debutant Peter Handscomb caught behind for 13 and then bowled Coulter-Nile on the final ball of the 19th over to keep the game hanging in balance.
Jhye Richardson and Cummins then kept their calm in the final six balls against Umesh Yadav to power their side home.
"It's a really strong position to be in," Australia skipper Aaron Finch said after the win.
"Nathan is a wicket-taker. He has been very consistent in the IPL as well," he added.
"Maxi (Maxwell) played a hell of an innings on a pitch which was tough to bat."
The day belonged to Coulter-Nile who returned figures of 3-26 in his four overs, receiving the man of the match award.
Indian batsman K.L. Rahul, who returned to the side after a suspension for controversial comments during a TV chat show appearance with Hardik Pandya, hit 50 off 36 balls.
His 55-run second wicket stand with skipper Virat Kohli, who made 24, gave India a brisk start but the hosts lost momentum after losing three quick wickets.
Adam Zampa got Kohli's prized scalp with his leg spin and Coulter-Nile claimed the wicket of Rahul to check India on a tricky pitch.
Veteran wicketkeeper-batsman Mahendra Singh Dhoni made an unbeaten 29.
"A low scoring game is always on the cards in T20 cricket," said Kohli.
"With the bowling effort we were pleased. Bumrah can do wonders with the ball when it is reversing and did exceptionally well to get us in the game," he added.
"Australia deserved to win as they played better than us."