Chris Jordan too came up with an economical spell, in which he claimed 2 wickets for 37 runs.
After Australia were reduced to 64/4, George Bailey came to their rescue with a knock of 56.
James Faulkner once again made good use of the long handle to contribute run-a-ball 27 to push Australia's final score to 217.
Stuart Broad provided the perfect start to England by dismissing Aaron Finch (7) and Shane Watson cheaply (0). He ended with figures of 10-2-31-3.
Alastair Cook scored 39 and added 61 for the third wicket with Joe Root to steady England run-chase after two early blows.
James Faulkner backed his useful contribution with the bat with a couple of wickets that kept Australia in the game.
Joe Root scored 55 and added 64 runs in partnership with Eoin Morgan to put England back on course.
Eoin Morgan scored 39 and but was dismissed James Faulkner to allow Australia a late sniff.