England only posted 130 for nine after winning the toss and the home side coasted to victory with 5.1 overs left at 131 for two.
Skipper George Bailey clubbed an unbeaten 60 off just 28 balls with three sixes and seven fours, while opener Cameron White continued his magnificent series with 57 not out off 45 balls.
England will finish their troubled tour of Australia in Sydney on Sunday in the final dead rubber T20 game after losing the Ashes 5-0 and the one-day series 4-1.
Fast bowler Josh Hazlewood was named man-of-the-match with career-best T20 figures of four for 30 in England's innings, including two wickets with his last two balls.
"Australia outplayed us fantastically today. They held length pretty well and we didn't react to that and the two needless run-outs hurt us in the middle which cost us getting a decent score," England skipper Stuart Broad said.
"We need to get some momentum from somewhere. It's been a long tour, it's been a long 100 days in Australia and it would be nice to finish with a win.
"We have not (win) a series over here which is heart-breaking for Team England, but we can finish on a high before we fly two hours later."
Australian captain Bailey said his side's bowlers had set up the win.
Bailey paid credit to Hazlewood and also 20-year-old leg-spinner James Muirhead (1-17 off 4 overs).
"James Muirhead bowled absolutely beautifully," Bailey said.
White posted his second successive half-century in his first T20 International series since October 2012 in a follow-up to his 75 in Wednesday's opening T20 match in Hobart.


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