Opener KL Rahul (55 off 35 balls) and Suryakumar Yadav (46 off 25) got the party going early, before Hardik Pandya (71no off 30) provided the late fireworks to propel India past 200.
Test skipper Cummins finished the match with figures of 0-47 off four overs, while Cameron Green copped some late punishment on the way to 1-46 off three overs.
Green was thumped for three consecutive sixes on the final three balls of the innings as Pandya sent the crowd wild and propelled India to their biggest T20 total against Australia.
Spinner Adam Zampa (0-36) also struggled, but pace duo Nathan Ellis (3-30) and Josh Hazlewood (2-39) fared better.
Glenn Maxwell produced the highlight moment in the field when he saved what was on track to be a certain six in the 19th over.
Maxwell leapt in the air and over the boundary rope to catch one-handed Harshal Patel's big hit.
Before he landed, Maxwell threw the ball back into the field of play, with India only scrambling through for a single instead of gaining six runs.
Virat Kohli, fresh off his drought-breaking century against Afghanistan in the Asia Cup, was dismissed for two off seven balls by Ellis.
India were 2-35 at that stage, but Rahul, Yadav, and Pandya combined for 13 fours and 12 sixes to put the home side back in the box seat.
Ellis was impressive in snaring the scalps of Kohli, Axar Patel and Dinesh Karthik.
Hazlewood removed openers Rahul and Rohit Sharma (11).
Green's day started well when he found the edge of Yadav, but the West Australian's last over of the innings cost 21 runs.
With Mitch Marsh and Marcus Stoinis not on tour due to injury, power hitter Tim David was named for his Australia debut.
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