The dynamic young pair came together with their side appearing to be heading for another defeat and losing the series as well.
England needed 84 runs from just over 11 overs when Ravi Bopara was out.
But Buttler (65 not out) and Stokes (25) managed to turn the game on its head.
Durham all-rounder Stokes was out near the end but Buttler remained and hit the winning runs with a boundary off Mitchell Johnson with three balls remaining for a three wicket win.
Chasing 228 to win, fast bowler Clint McKay's stunning hat-trick at the start of the England innings had put Australia well on top.
The big Aussie fast bowler was called into their side as a late replacement -- and then left Kevin Pietersen, Jonathan Trott and Joe Root embarrassed as they limped slowly back to the pavilion.
Michael Carberry (63) and Eoin Morgan (53) led the recovery before both they and Ravi Bopara fell.
But Buttler and Stokes were waiting to become the stars of the hour.
And then slow bowler James Tredwell found his form late in the innings to take three wickets as Australia were bowled out for 227 off 48.2 overs.
But they had had their rivals on the ropes only to lack the know how or ability to tighten their grip on the match with vice-captain George Bailey saving his side from complete disaster with 87 from 91 balls.
Finn (2-43), struggling to rediscover some of his old form, did show real pace and zip with the Middlesex star removing opener Aaron Finch second ball.
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