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Put in to bat, Australia scored a challenging 194 for 5 with skipper Matthew Wade top-scoring with a quick-fire 32-ball 58 while Steve Smith contributed 46 off 38 balls.
India chased down the target in 19.4 overs overs with Hardik Pandya remaining not out on 42 off just 22 balls. Shikhar Dhawan contributed 52 while captain Virat Kohli made 40.
India had won the first T20I by 11 runs in Canberra on Friday. The inconsequential third T20I will be played here on Tuesday.
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Australia: 194 for 5 in 20 overs (Matthew Wade 58, Steve Smith 46; T Natarajan 2/20).
India: 195 for 4 in 19.4 overs (Shikhar Dhawan 52, Virat Kohli 40; Hardik Pandya 42 not out; Mitchell Swepson 1/25)