It was a deserved victory for a powerful Australian side, who struck 14 boundaries to England's eight on a vast Melbourne outfield.
Mitchell Johnson took 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.
Despite their losing streak, Australia did not look a team short of confidence as, after winning the toss and choosing to bat, they got off to a bright start with the powerful duo of David Warner and Shane Watson tucking into the bowling of Woakes and Ajmal Shahzad.
The consistent Watson picked up where he left off in Adelaide with two huge sixes, but he came unstuck in Woakes' third over when a leg-sided swipe went straight to Eoin Morgan in the deep.
The wicket did not stem the flow of runs, with Tim Paine smashing his second ball for six over mid-on as Australia reached a healthy 57-1 off the first six-over power play.
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 for 17 in runs in the next five overs.
Swann repeated his uncanny knack of taking a wicket in the first over of a spell as Paine top-edged a slog-sweep to Collingwood, who recovered from an uncharacteristic fumble to bag 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.
Ian Bell was impressive with the bat once again for England
Swann continued to peg the Aussies back at the other end, conceding only 12 runs from his first three overs and trapping Australia captain Cameron White leg before wicket for none.
David Hussey struggled to make an impact, labouring to eight from 16 balls before gifting Yardy his second wicket of a superb four-over spell, the Sussex man finishing with 2-19 - exactly the same figures as Swann.
Finch and Steven Smith did their utmost to rebuild the Australia innings, without ever really getting on top of the English bowling.
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.
Chasing 148 to win, England made a solid start with Bell hitting two fours from Shaun Tait's first over and keeping the scoreboard ticking over with some neat strokes.
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 pulled to the rope by Bell.
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, took another catch.
Luke Wright kept England in the game with 18 from 15 balls before he was well caught by Smith.
At that point, England's hopes of victory appeared to rest with their expert finisher Eoin Morgan, but the left-hander came unstuck when a heave off Johnson picked out Finch at deep midwicket.
With Morgan gone, the game was effectively up, but there was still time for Woakes to provide England selectors with a reminder of his talents ahead of the seven-match one-day series, which starts on Sunday.
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