Australia made a blistering start to their chase of 310, with openers Matthew Short (58) and Head (31) sharing a stand of 78 in slightly more than seven overs.
And when rain stopped play, Australia was 165-2 off 20.4 overs well ahead of the target required under the Duckworth-Lewis-Stern (DLS) method.
Steve Smith, leading Australia in place of the injured Mitchell Marsh, was 36 not out before the umpires called the game off at 6:00 pm local time (1700 GMT).
Australia’s opening batters Short and Head punished a wayward England attack featuring Olly Stone, in for the rested Jofra Archer. But Brydon Carse struck with his first ball when he had Travis Head caught at cover.
Matthew Potts, who had already dismissed Australia’s Smith twice in the series, almost had the star batter given out lbw for 10 but a review indicated the ball would have missed leg stump.
Short went to fifty when he pulled Carse for his fourth six in just 23 balls. But he was out when caught behind driving at Potts.
England then missed an opportunity when they didn’t appeal after Josh Inglis, on two, got a thin edge off Carse to wicketkeeper Jamie Smith.
Earlier, Steve Smith won the toss only for Phil Salt to launch England’s innings with a quickfire 45 that featured consecutive sixes off Aaron Hardie.
But Hardie had his revenge when Salt’s drive over point was caught by Marnus Labuschagne before he bowled Will Jacks for a duck with an excellent off-cutter.