The visitors got off to a strong start, surging to 1-97 off 9.4 overs when the heavens opened in Canberra on Wednesday night.
The match had already been shortened to 18 overs apiece after a 45-minute stoppage earlier in the innings.
After being sent in by Australia captain Mitch Marsh, India's openers raced to 35 off 3.5 overs before Abhishek Sharma (16) mistimed a wild drive off the bowling of Nathan Ellis to Tim David at mid-off.
A 62-run partnership between captain Suryakumar Yadav (39 not out) and opener Shubman Gill (37no) had India in a commanding position as the innings passed its midway point.
Australia should have dismissed Suryakumar for 20 after the India captain spooned a straight drive above mid-on.
But NSW wicket-keeper Josh Philippe, brought into the national side for the first time in two years as a specialist batter, failed to clasp a challenging catch with the ball dropping over his shoulder as he ran back towards the boundary.
Suryakumar made Australia pay two overs later, smashing Ellis for two fours and a six off before the return of the rain sent the players and umpires running for cover for good.
A sold-out crowd of mostly India fans were denied the sight of fast bowling superstar Jasprit Bumrah, while Marsh was unable to press his outside hopes of an Ashes call-up, as Australia selectors mull who will partner Usman Khawaja at the top of the order.
Australia were full of confidence after winning the three-match one-day international series between the two sides 2-1, but face a tough prospect of claiming victory in the remaining four matches against the reigning T20 world champions.
The teams will hope the weather will be more obliging for the second game of the series at the MCG on Friday.
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