Leg-spinner Adam Zampa shone with the ball to help Australia register a narrow four-run victory against India in the rain-hit first T20 International in Brisbane on Wednesday.
All-rounder Stoinis stroked an unbeaten 33 from 19 balls and then claimed two wickets in the final over as India finished on 169 for seven in 17 overs, to lose by four runs via the Duckworth-Lewis method.
Shikhar Dhawan had rallied India after the early dismissal of Rohit Sharma (7) as he smashed a quickfire 76 from 42 balls.
But the quick dismissals of KL Rahul (13), Virat Kohli and Dhawan saw India lose their way in the middle overs.
It was leg-spinner Adam Zampa, who made the difference with the ball, as he bowled a splendid spell of two for 22 in four overs, including the key wicket of Kohli.
Dinesh Karthik kept India alive as he slammed 30 from 13 balls but Stoinis kept his composure in the final over and prevented India from getting the 13 runs required for victory.
Earlier, Glenn Maxwell smacked 46 runs off 24 balls to fire Australia to 158 for four in 17 overs.
A spell of heavy rain cut the game short to 17-overs a side after which the target for India was revised to 174 runs via the Duckworth-Lewis method.
Maxwell hit four sixes in his whirlwind knock before rain halted play, after Chris Lynn scored 37 runs off 20 balls to help Australia recover from a slow start.
This was after India won the toss and opted to bowl on a surprisingly green wicket. Kuldeep Yadav was picked ahead of Yuzvendra Chahal as expected, while the hosts also included a spinner in Adam Zampa and left out medium pacer Nathan Coulter-Nile.
Bhuvneshwar Kumar and Jasprit Bumrah kept Australia's openers in a tight leash in the early over before captain Aaron Finch (27) pulled things back a bit. Khaleel Ahmed (1-42) got the initial breakthrough as D'Arcy Short (7) was caught at long on but the young left-arm pacer proved expensive thereafter.
Kuldeep took a sensational catch running back to dismiss Short to help India make the first breakthrough.
Kuldeep was superb with the ball as he registered wonderful figures for 2 for 24 in his four-over spell. He dismissed Finch and then sent back the dangerous Lynn as well, reducing Australia to 75-3 in the 11th over.
India were rather poor in the field as they put down a couple of catches. Skipper Virat Kohli dropped Finch in the fourth over, a straight chance spilled at cover, before Khaleel Marcus Stoinis (33 not out off 19 balls) late in the Australian innings, while Rahul missed an easy chance to run out Maxwell.
Finch took advantage of the reprieve and put on 40 runs off 26 balls with Lynn for the second wicket.
But it was Maxwell who stole the show with his belligerent hitting as Australia crossed 150 in the 16th over. He put on 78 runs off 37 balls with Stoinis as Indian bowlers proved expensive even before the death overs began.
Krunal Pandya went for 0-55 in his four overs before rain intervened and nearly 45 minutes were lost owing to stormy conditions. The match was curtailed thereafter, sucking out momentum from the Australian innings and leaving them only five deliveries on resumption of play.
Bumrah bowled cleverly, conceding only five runs from the remaining five deliveries after the resumption of play helping the hosts post a challenging total.