Needing 14 runs off the final over, bowled by Umesh Yadav, Pat Cummins and Jhye Richardson each hit a boundary before they scampered to complete two runs off the last ball to reach their target of 127 in a nail-biting contest.
Fast bowler Nathan Coulter-Nile took three wickets on his return to limited-overs cricket as Australia beat India by three wickets with the final delivery in a low-scoring first Twenty20 international at Visakhapatnam on Sunday.
Needing 14 runs off the final over, bowled by paceman Umesh Yadav, Pat Cummins and Jhye Richardson each hit a boundary before they scampered to complete two runs off the last ball to reach their target of 127 in a nail-biting contest.
Fast bowler Jasprit Bumrah, who was rested for India's limited-overs trip to New Zealand, took 3-16, including two wickets in his final two deliveries in the penultimate over, but it proved inadequate.
Coulter-Nile led a strong bowling display by the touring side with 3-26 in his four overs as Australia restricted India to a paltry 126-7 in the first of the two-match series after captain Aaron Finch won the toss and chose to field.
Australia also got off to a shaky start and were reduced to 5-2 before Glenn Maxwell and D'Arcy Short combined in a third-wicket stand of 84 to steady the chase.
Maxwell hit 56 off 43 balls, his innings studded with six fours and two sixes. Short, who opened the innings for Australia with Marcus Stoinis, was run out for 37.
After Maxwell's dismissal, India fought back spectacularly to reduce Australia to 113-7 from 89-2 before the thrilling last-over finish.
With the 50-over World Cup coming up in three months' time in England and Wales, India opted to give Lokesh Rahul an opportunity at the top of the order by resting regular opening batsman Shikhar Dhawan.
Rahul, who was recently provisionally suspended for inappropriate comments on a TV chat show, did no harm to his chances with a 36-ball 50 and combined in a quickfire stand of 55 for the second wicket with Virat Kohli, who made 24.
Adam Zampa got the prized wicket of the Indian captain, who holed out to Coulter-Nile at long on trying to hit the leg-spinner for a six.
Coulter-Nile played just one ODI in 2018, against South Africa, and missed out on selection for the home limited-overs series against India.
He has the ideal opportunity to improve his chances of making the World Cup squad in the absence of the injured Mitchell Starc and Josh Hazlewood in India.
The 31-year-old dismissed Rahul and Dinesh Karthik in the same over and then added the wicket of Krunal Pandya as India were reduced to 100-6 in the 15th over.
Former captain and wicket-keeper Mahendra Singh Dhoni laboured to a 29 off 37 balls and failed to boost India's score despite farming most of the strike in the closing stages of India's innings.
The second and final T20 will be played in Bengaluru on Wednesday.