Dawid Malan cracked 50 off 36 balls with five fours and two sixes but England fell away after reaching 94 for two in the 10th over.
Glenn Maxwell captured three for 10 and Ashton Agar took two for 15 as Australia sent England's middle order tumbling.
Kane Richardson (1-27) removed dangerous opener Jason Roy for nine, before Malan hit a lively half-century.
Malan was supported by Alex Hales with 22 from 15, and captain Eoin Morgan, also 22 from 14 balls.
Jos Buttler (5) fell cheaply to be caught by Maxwell off Marcus Stoinis (1-16), while Billings (10) popped a return catch to Agar.
Malan was caught in the deep by Andrew Tye for Maxwell's second wicket and David Willey (3) was recklessly stumped next ball to give Alex Carey his first international stumping.
Maxwell's hat-trick ball was wide of the leg-stump line.
Adil Rashid (1) got the toe end of the bat on a shot off paceman Billy Stanlake and was well caught by Stoinis, while Tom Curran (6) was well held by a back-pedalling Warner after failing to pick Tye's knuckle ball.
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