But an otherwise routine win was overshadowed when England all-rounder Ben Stokes was controversially given out obstructing the field -- a dismissal greeted by jeers round Lord's.
Sent into bat, world champions Australia made 309 for seven in a match reduced by rain to 49 overs per side, captain Steven Smith top-scoring with 70 and all-rounder Mitchell Marsh making 64 towards the end of the innings.
England in reply saw captain Eoin Morgan, infuriated by Stokes's dismissal, top-score with 85 before he was last man out in a total of 245.
The series continues at Old Trafford on Tuesday.
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Brief scores
Australia: 309-7, 49 overs (S Smith 70, M Marsh 64, G Bailey 54; B Stokes 3-60)
England: 245, 42.3 overs (E Morgan 85; P Cummins 4-56)
Result: Australia won by 64 runs
Series: Australia lead five-match series 2-0.