The Australians were always in the box seats, with the tourists on 176 for nine with an over left. (Agencies)
But some prodigious late hitting by Ravi Bopara got England to within 13 runs of the target at the finish.
Bopara smashed seven sixes and two fours in his unbeaten 65 off 27 balls but paceman Nathan Coulter-Nile bowled the Australians to victory with four for 30 off his four overs.
Joe Root scored 32 off 24 balls and opener Alex Hales hit 22 off 12 balls for the beaten tourists, who have only won one limited-over international on their hapless tour of Australia.
Australia won the Ashes Test series 5-0 and the ODI series 4-1 before the three-game T20 series began.
"Ravi's performance was a positive, but if you lose three wickets in the first six overs you rarely win," said England skipper Stuart Broad.
"We'll reflect and consider changes, but I err on the side of consistency and back these players to come back strong in Melbourne."
Cameron White was named man-of-the-match for his 75 off 43 balls as Australia set England 214 to win.
England's previous highest T20 run chase was 181 against India in 2012 so their 200 for nine was their highest score in the format.
White, recalled by Australia for the first time since 2012, smashed six boundaries and four sixes to set the platform for the home side's 213 for four after they won the toss.
White put on 106 with opening partner Aaron Finch (52 from 31) as the Australians came out with all guns blazing.
"It's a nice feeling to be back and it's something I've worked hard for, to get the opportunity playing for Australia since I last played," White said.
"England are a dangerous side and they bat really deep in the order, and with the short boundaries here at Bellerive the game was never really won. Ravi batted really well."
Finch hit three sixes and five fours as the pair reached a century partnership off 59 balls.
He was caught in the deep in the 11th over, while it took the most eventful over of the innings to claim White.
The over brought 18 runs off the bowling of Luke Wright and looked also to have claimed White's wicket when he skied to Danny Briggs at fine leg.
However a no-ball was called. The third umpire took several looks at the replays at Wright's full toss to confirm it was above waist height and White survived.
But White was dismissed leg before wicket before the over was completed and Australia were 134 for two.
Glenn Maxwell (20 from 13) produced an astonishing reverse sweep for six off Briggs, but the shot proved to be his downfall when he was caught at 157 for three.
Australia could not sustain their early pace until, on debut, Chris Lynn cracked three sixes in his late cameo of 37 from 19. Dan Christian was six not out.
The second game in the three-match series is in Melbourne on Friday.
The Australians were always in the box seats, with the tourists on 176 for nine with an over left.