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England chased down the modest target of 126 with 8.2 overs to spare, with Jos Buttler top-scoring with 71 not out while Jason Roy contributed 22.
For Australia, Ashton Agar and Adam Zampa took a wicket each.
Earlier, invited to bat, the Australians suffered a batting collapse with captain Aaron Finch top-scoring with a 49-ball 44 while Ashton Agar contributed 20.
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Brief Scores: Australia: 125 all out in 20 overs (Aaron Finch 44; Chris Jordan 3/17, Tymal Mills 2/ 45, Chris Woakes 2/23).
England: 126 for 2 in 11.4 overs (Jos Buttler 71 not out; Ashton Agar 1/15)