On a Bridgetown deck where runs flowed easily, legspinner Adam Zampa (2-28) was a game-changer for Australia, dispatching openers Jos Buttler and Phil Salt after they made a fast start in pursuit of 202 in Barbados on Saturday (Sunday AEST).
Earlier, Australia's openers David Warner (39 from 16 deliveries) and Travis Head (34 from 18) had laid the groundwork for the side's 7-201 - the highest total at the tournament to date.
After winning the toss, England were left to rue letting Warner and Head off the leash early, finishing their 20 overs at 6-165.
David Warner got Australia off to a blistering start in their Bridgetown innings. (AP PHOTO)
The win keeps Australia undefeated through two matches at the World Cup and means they will top Group B if they beat minnow nations Scotland and Namibia in their final two games before the Super 8 stage.
"I'm very pleased with that effort," said Australia captain Mitch Marsh.
"I thought our all-round game was outstanding. Our experienced players shone when we needed them."
England, meanwhile, are still searching for their first win of the tournament after their opening hit-out against the Scots was washed out and they can't afford anything less than victory against Oman next Friday (AEST).
"(Australia) came out with a lot of intent and played really well," said Buttler.
"They put us under a lot of pressure straight away, had a good power play, It was tough to drag it back from there."
Australia left England requiring the third-largest successful run chase in tournament history but they appeared up for the task as Buttler (42 from 28 deliveries) and Salt (37 from 23) matched the heroics of Australia's own opening partnership.
Australia's seamers struggled on a pitch that made life hard for the quicks all day, especially with the new ball.
But Zampa had an immediate impact once injected into the attack after the English openers had exposed the short boundary and punished Mitch Starc (0-37) and Josh Hazlewood (1-28) across their 73-run stand.
With his first delivery of the day, Zampa sent a length ball into Salt's off stump, saving Head's blushes after he had put his foot on the boundary rope catching the opener an over earlier.
Zampa continued to hit excellent lengths and was rewarded with the pivotal wicket of English captain and the game's top-scorer Buttler, who picked out Pat Cummins (2-23) at backward point on the quick's return to the T20 side.
Moeen Ali (25) threatened to hoist England back into the game with three sixes from the same Glenn Maxwell (0-22) over, but 'The Big Show' exacted his revenge when he caught slumping Jonny Bairstow (seven) at deep mid-wicket from Josh Hazlewood's bowling.
Maxwell taunted the pro-England crowd after the wicket, aware that at 4-124 in the 15th over, the game was slipping out of England's reach.
Following a scintillating IPL, Cummins (2-23) had the most success of the quicks to ensure the English were never able to get going again once he dismissed Ali.
Glenn Maxwell never quite got going for Australia even as they racked up 7-201. (AP PHOTO)
Earlier, Buttler's call to open the bowling with two offspinners backfired.
Warner and Head helped themselves to 22 runs from part-time tweaker Will Jacks in the second over to set the tone for their 70-run partnership.
There were visible moments of frustration from a number of individuals as Buttler's side lacked precision, with Zampa hinting that the flurry of boundaries from Head and Warner had unsettled their opponents.
"I think they were under the pump and it showed," Zampa said.
"It's so hard to bowl to us in the powerplay and if your bowlers aren't summing it up quickly enough it can be frustrating."
Anything too quick was also easily dispatched, with retiring Warner feasting on Mark Wood (0-32) in likely his last appearance against England.
Once England cottoned on that pace would not win the day, they had the openers within five balls of each other, offspinner Ali (1-18) first bowling Warner as he misplayed a cut shot.
When injury-plagued quick Jofra Archer (1-28) took pace off and completely dislodged Head's middle stump, England had steadied the ship at 2-74.
But Marsh (35) and Maxwell (28) kept Australia on track, albeit without going on to big scores themselves and a dream total was confirmed through a 30-run cameo from Marcus Stoinis at the death.
With PA.
