The match went to the last ball but Tim Bresnan could only manage a single when a six would have snatched a win.
Finch made 53 not out off 33 balls on a slow pitch as the hosts, batting first, recovered from 80-5 to post 147-7.
Ian Bell (39) gave
That had become 13 from three when Chris Woakes, England's debut hero in Adelaide two days earlier, smashed Brett Lee for six over long on to ignite hopes of a last-gasp turnaround.
But a mistimed pull off the next delivery brought just a single run, and Bresnan could only pick out deep extra cover with his attempted heave off the final ball.
It was a deserved victory for a powerful Australian side, who struck 14 boundaries to
Mitchell Johnson then claimed three wickets and Shane Watson posted a miserly spell of 2-17 from his four overs as the hosts ended their own dismal run of five straight Twenty20 defeats to draw the series 1-1.
After winning the toss and choosing to bat,
The consistent Watson picked up where he left off in
The wicket did not stem the flow of runs, with Tim Paine smashing his second ball for six over mid-on as
With his pacemen struggling, Paul Collingwood turned to his spin duo of Michael Yardy and Graeme Swann and the tactic paid dividends as four wickets fell fir 17 in runs in the next five overs.
Swann repeated his uncanny nack of taking a wicket in the first over of a spell as Tim Paine top-edged a slog-sweep off to Collingwood, who recovered from an uncharacteristic fumble to claim the catch at the second attempt.
Not to be outdone, Yardy struck with his second ball as an off-balance Warner picked out Kevin Pietersen at long-on to fall for 30.
Swann continued to peg the Aussies back at the other end, conceding only 12 runs from his first three overs and trapping
David Hussey struggled to make an impact, labouring to eight from 16 balls before gifting Yardy his second wicket of a superb spell, the
Finch and Steven Smith did their utmost to rebuild the
Finch was the more fluent of the pair, smashing one straight six off Pietersen and scooping a Shahzad delivery over his own head to the fine leg boundary.
The partnership had passed 50 when Smith slapped a slower ball from Shahzad to Collingwood at mid-off, and he was swiftly followed by Steve O'Keefe, who was bowled after his own attempt at a scoop shot failed miserably.
Finch accelerated impressively thereafter, smashing Shahzad for a four and a six in the 19th over and striking each of the last four balls for two to bring up his half-century.
Johnson, an erratic performer throughout the Ashes series, looked out of sorts early on as he fired a wide down the off side before a long-hop on leg stump was heaved over the ropes by
Bell picked up two more from the first ball of Johnson's next over before a quicker, straighter, ball from the left-armer caught the inside edge of his bat and flattened his stumps.
Three balls later, Pietersen took a swing at a wider ball and Cameron White clung on to a sharp low catch in the covers.
Collingwood's miserable run with the bat continued, the skipper posting a scratchy six before trying to drive over the top and spooning a simple catch to David Warner.
Steven Davies, starved of the strike for much of his innings, never looked fluent in his innings of 29, his demise coming in similar fashion to Collingwood as Warner, diving forward, claimed another catch.
Luke Wright kept
At that point,
With Morgan gone, the game was effectively up, but there was still time for Woakes to provide