England were set for a huge total when opener Ben Duckett (107) and in-form captain Harry Brook shared a third-wicket stand of 132 in 98 balls.
But from 202-2, slow bowling proved England's undoing as they lost their last eight wickets for 107 runs to be dismissed for 309, with part-time spinner Head taking an ODI best 4-28.
Australia made a blistering start to their chase, 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 were 165-2 off 20.4 overs - well ahead of the target required under the Duckworth-Lewis-Stern method for weather-affected white-ball games.
Steven Smith, leading Australia in place of the injured Mitchell Marsh, was 36 not out before the umpires called the game off at 18:00 BST.
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 left-hander Head caught at cover.
Matthew Potts, who had already dismissed Australia's Smith twice in the series, almost had the star batsman 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.
Brook and Duckett run riot
Brook came in having struck a maiden and match-winning ODI century at Chester-le-Street on Tuesday that helped reduce England's deficit to 2-1 before his 87 laid the foundation for a colossal 186-run success at Lord's on Friday.
The 25-year-old Yorkshireman audaciously scooped experienced fast bowler Josh Hazlewood for four.
Duckett, who made 63 at Lord's, completed a 45-ball fifty before Brook reached the landmark in just 39 balls when he drove Hardie over long-on for six.
Brook then struck leg-spinner Adam Zampa for successive sixes at the start of the 25th over.
But Zampa, holding his nerve, deceived Brook four balls later with a slower, flighted delivery the batsman miscued low to Glenn Maxwell at long-off.
Zampa finished with an expensive 2-74 from his full 10 overs.
Brook's exit sparked an England slump but Duckett, out for 95 in the series opener at Trent Bridge, completed his second career ODI hundred - both made at Bristol - in 86 balls including 13 fours and a six.
The left-hander's first England century in all formats this season, after several close calls in both Tests and ODIs, ended soon afterwards when he holed out off Head.
