The Australians were always in the box seats, with the tourists on 176 for nine with an over left.
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.
"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.
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