Instead it was a stunning effort from India's comeback kid Yuvraj Singh which allowed the home side to win the one-off T20 game, chasing down Australia's target of 202 with two balls to spare.
But if not for one crucial moment falling in India's favour, Australian captain George Bailey felt his side would've finished in front.
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Singh only offered one chance in his unbeaten match-winning 77, which powered India to a six-wicket victory.
With Clint McKay bowling, Singh flicked a length delivery of his pads and seemingly over the fence for one of his five sixes in the outstanding 35-ball innings.
Shane Watson, fielding on the deep square leg boundary, spectacularly fielded the ball over the rope and attempted to acrobatically fling it in the air to regather in the field of play.
But he was unable to plant his feet inside the rope before regathering the ball.
"(It's a) game of inches," Bailey said after the match.
"Watto nearly catches him on the fence there and that's a different game.
"...If we could've found a way to take a wicket that would've changed everything as well.
"Particularly Yuvraj. If we could've forced a wicket (it changes everything).
"And we were close, we (almost) had him caught on the fence a couple of times. But just couldn't manage it."
Earlier, after being sent in, Australia posted 7-201 on the back of an excellent 89 from Finch, who was ably supported with cameos from Glenn Maxwell (27 off 13) and debutant Nic Maddinson (34 off 16).
Just as he did with his world record 156 against England in August, Finch combined the brutal with the unorthodox to send India's attack to all parts of the boundary.
Ultimately his 14 fours and one six pieced itself together as a composed knock of 89 as Australia passed 200 for just the sixth time in T20s.
It took a spectacular caught-and-bowled from Vinay Kumar (3-25) to halt the powerful right-hander.
"As disappointing as it is to lose there were some real positives to come out of it," Bailey said.
"Finchy was outstanding again, Nic Maddinson right behind him which was great to see.
"Maxy played beautifully.
"...There were some positives in amongst the disappointment of losing."
For Australia, the seventh ranked T20 nation, the loss was the seventh from the past eight matches.
The feeling of letting a victory slip away would be amplified by the fact they had India at 4-100.
That was when skipper MS Dhoni (24no) arrived at the crease, with his unbeaten 102 run partnership with Singh sealing Australia's fate.
"We've had long partnerships in the past," Singh explained.
"We have a very good understanding between us."
The teams now prepare for seven one-day matches.