Australia 4 for 158 (Maxwell 46, Kuldeep 2-24) beat India 7 for 169 (Dhawan 76, Zampa 2-22) by four runs on DLS method.
Australia held on for a thrilling victory over India in the first Twenty20 international in Brisbane.
Australia overcame India and their own considerable self-doubts to claim a white-knuckle Twenty20 encounter at the Gabba, having granted India a late sight of victory in a rain shortened affair.
Marcus Stoinis successfully defended 13 off the final over, after at one point India had required 70 from 32 balls.
Chasing 174 from 17 overs, India needed 13 from the final over but Marcus Stoinis took two wickets in consecutive balls to secure victory by four runs.
Glenn Maxwell scored 46 as the hosts made 158-4 amid a rain interruption and India were set a revised total via the Duckworth Lewis Stern method.
Maxwell smacks four sixes in brutal knock:
Shikhar Dhawan hit 76 and Dinesh Karthik 30 but India fell just short.
Dhawan’s brilliant innings, which included two sixes and 10 fours, had given the tourists hope in their difficult chase but when he fell with the score 105-4, Australia were clear favourites.
India needed 60 runs from the final four overs but Karthik and Rishabh Pant gave India the edge with a blistering fifth-wicket partnership of 51 from 24 balls, which included hitting seamer Andrew Tye for 25 runs in the 14th over.
However, Pant fell for 20 in the penultimate over and Karthik was the second of two wickets in two balls in the final over as he tried to clear the ropes with India needing 11 runs off the final three deliveries.
Earlier, Australia capitalised on some poor India fielding, with Virat Kohli dropping Australia captain Aaron Finch, who went on to make 27, while Maxwell hit three sixes after KL Rahul missed a straightforward opportunity to run him out.
Australia lead the three-match series 1-0 with the second match taking place on Friday in Melbourne.