England 182 for 5 (Morgan 74, Moeen 72) beat Australia 177 for 8 (Smith 90) by five runs
Scorecard and ball-by-ball details
In years to come, people will look at the scorecard of this match and presume that Ben Stokes - with modest bowling figures and a peripheral figure with the bat - played nothing more than a supporting role in this game.
But Stokes, with an outstanding catch and a nerveless final over, played a key part in an England victory that continues a remarkable summer that promised little more than pain and has delivered more promise and encouragement than even the most optimistic supporters could have anticipated.
After a grim 2014 when they lost nine of their 12 T20Is, including a wretched World T20 campaign, new-look England have now won three in a row and have defeated the No. 2 ranked side. Their limited-overs resurgence, a development that looked most unlikely when they were knocked out of the World Cup at the first hurdle only a few months ago, continues.
More importantly, with players such as Stokes involved, they appear to be developing into a team that relishes pressure moments. While some previous England sides have appeared to wilt in the spotlight, here they held their nerve under pressure to secure a five-run victory.
With seven overs to go, it appeared Australia were cruising. Glenn Maxwell and Steven Smith, with his maiden T20I half-century, had added 112 for the third-wicket and the previous four overs had cost 13, 10, 14 and 14 respectively.
But then Maxwell attempted to pull Moeen Ali's first ball, little more than a dragged-down long-hop really, for six over mid-wicket only to see Stokes, dashing round from long-on, leap to his right and cling on to an outstanding catch.
It was the moment that changed the game. Reece Topley, impressively calm for a 21-year-old on international debut, bowled Mitchell Marsh with a nicely disguised slower-ball delivered out of the back of the hand before Smith miss-hit to mid-on. Nerves spread through the Australian line-up and with Stokes delivering a fine final over - Australia could manage just six of the 12 runs they required for victory from it - they lost five wickets for 16 runs in the final 14 balls of the innings.
Stokes is not the only one in this new-look England side that seems to relish the big occasion. His captain, Eoin Morgan, has struggled so badly in county cricket that it was decided to rest him for a month prior to this match
But here, coming to the wicket with his side struggling to make progress against Australia's impressive pace attack, he looked a high-class T20 player in thrashing 74 from just 39 balls. It was an innings that largely vindicated his decision to rest.
"I've been practising for the last 10 days and it's been really good," he said. "I feel fresh mentally and physically.
"I've never asked for a break before. It had been 11-months without one and, if I'd known I'd be so busy in October, I'd have asked for one before. It's worked out well."
With Moeen, who made a career-best T20I score of 72 not out and was given his first international Man of the Match award, Morgan added 135 in 12.2 overs for the third-wicket - England's fourth highest T20I partnership - to help them recover from a lacklustre start that yielded only 27 runs and two wickets from the Powerplay.
At that stage, the Australian attack looked daunting. Pat Cummins, generating fierce speed (he averaged 91 mph), beat Alex Hales for pace with a full toss and then had Jason Roy taken at mid-off as he tried to hit over the top.
But life became easier once the support bowlers were introduced into the attack immediately after the Powerplay. Moeen, unhurried and elegant, drove Marsh's first delivery over extra cover for four and then took 13 off Marcus Stoinis first over in international cricket.
Stoinis' was a somewhat puzzling selection. Having only played nine T20 games in his entire career - he was injured for the last Big Bash season - and delivered just five overs, his attempt to bounce Moeen was greeted by a pulled six, while the next delivery was dragged over mid-wicket for four more. He was withdrawn from the attack after the over and not seen again.
Morgan, while less elegant than Moeen, was every bit as effective. Skipping down the wicket to Shane Watson, he clubbed one six - with both feet off the ground - over the bowler's head for six, before taking three sixes of the bowler in his next over: anything on a good length hit over the top; anything short clubbed over mid-wicket. With Moeen taking a liking to the sedate legspin of Cameron Boyce, who is not part of the one-day squad, the pair added 41 in two overs at one stage.
By the time Cummins was reintroduced into the attack, Morgan was in full flow. A slower ball full toss was carved for one six before the next delivery, a short ball, was pulled for six more.
While the impressive Nathan Coulter-Nile ended Morgan's fun, Jos Buttler contributed 11 from four balls and, while England could managed only one more boundary from the final 16 balls of their innings, the target they set - 183 to win - had only been achieved once by Australia (against Pakistan in the memorable World T20 semi-final in 2010) in their T20I history.
Still, Morgan admitted he was "disappointed we didn't get 200" and "disappointed we didn't finish better."
Australia lost both openers early. David Warner was caught at third-man off the leading edge, again attempting to punch a short ball into the leg side, before Watson, to the obvious amusement of the England team, was bowled after the ball trickled back on to his stumps from a defensive shot and he missed his attempt to kick it away: an ironic end given how many times he has been dismissed due to his feet
However, Smith, batting in the top three for the first time in T20Is, looked imperious on a surface offering the bowlers little lateral movement and Maxwell demonstrated a maturity to complement his talent with a well-paced 44.
It was hard to believe that Smith's average in his previous 21 T20Is was just 14 as he drove Steven Finn for one glorious six and then swung him for another vast one into the pavilion.
Stokes' catch ended the partnership, though, and with Smith lacking support and England proving the calmer side, Australia's chase fell away.
"Moeen and Morgan got it over the fence quite a bit which is what you need," Smith said. "And our bowlers didn't execute as well as they would have liked. England have played some very good ODI cricket of late.
"Stoinis will be better for the run - everyone is nervous in their first game - and Boyce bowled well in Dubai, where the conditions will be similar to the World T20 in India. It was quite hard going for him, but he will learn and continue to get better."