Yuvraj forged an unbeaten 102-run stand with skipper Mahendra Singh Dhoni, who played a second-fiddle, as India chased down a huge 202-run target with two balls to spare.
Yuvraj carried his sublime form, with which he forced his way into the team, into the game as he plundered eight fours and five sixes in his 35-ball knock.
The left-hander whacked the bowlers all around the park as his trademark powerful flicks, ferocious cuts and elegantly lofted drives enthralled the packed house even as the Australians watched helplessly.
Aaron Finch had powered Australia to a challenging 201 for seven with his blistering 89-run knock off 52-ball as visiting batsmen made merry on a flat wicket after being invited to bat at SCA stadium.
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Finch plundered 15 boundaries, including a six, as he anchored the Australian innings while debutant Nic Maddinson (34) and Glenn Maxwell (27) also played more than handful knocks for their side.
An off-colour R Ashwin and Ishant Sharma bled 93 runs in six wicket-less overs between them and that cost India dearly. However, the wicket had nothing for the bowlers even as they bowled poorly.
However, India batsmen made up for the poor first half with some excellent batting even though the start was not that good as Rohit Sharma (8) exited early and Suresh Raina (19) could not build on to a good start.
Dhawan was stumped off Xaviwer Doherty while Kohli was caught off Clint McKay even as India reached 100 in 11 overs.
Dhoni and Yuvraj then turned it on with their scintillating batting.