Mitchell Johnson again proved a thorn in England's side, the left-arm paceman taking one wicket for 20 runs in five overs and twice seeing close lbw decisions against Jonathan Trott overturned in the batsman's favour. (Agencies)
When the umpires took the players off the field at 3:34pm local time, Trott was 28 not out on his Warwickshire home ground and stand-in England captain Eoin Morgan five not out.
A minimum of 20 overs per side were needed for a result to be declared under the Duckworth/Lewis method but, with the rain coming down ever harder, the umpires abandoned the match at 7:05pm.
Earlier Australia, 1-0 up in the five-match series following their crushing 88-run win in the second ODI at Old Trafford on Sunday after Friday's opener at Headingley was washed out, saw captain Michael Clarke win the toss and field.
Ashes-holders England, criticised by former captain Michael Vaughan for resting five senior players this series, were unchanged from the side beaten so heavily in Manchester.
But the overcast conditions prompted Australia to bring in an extra seamer in Josh Hazlewood in place of leg-spinner Fawad Ahmed.
Kevin Pietersen, opening alongside Michael Carberry in the absence of Alistair Cook and Ian Bell, whipped the fourth ball of the innings, from Clint McKay, from well wide of off stump for four through midwicket.
However, two balls later, England lost their first wicket. Carberry, desperate for runs after making just 10 against Ireland and four at Old Trafford following his international recall, was run out by yards when Pietersen set off for a needlessly tight single only for bowler McKay to gather the ball and run in to demolish the stumps.
Pietersen then fell for six when he failed to get over the top of a Johnson bouncer and pulled a gentle catch straight to George Bailey at square leg.
Trott was on 13 when he was given out lbw to Johnson after aiming across the line. But he reviewed English umpire Michael Gough's verdict and was reprieved when the Decision Review System (DRS) indicated the ball had just pitched outside leg stump.
Johnson then challenged Gough's decision when Trott, now on 20, was given not out in response to the Australian's lbw appeal only for an 'umpire's call' ruling to rescue the South Africa-born batsman.
Trott was then hit on the helmet when he missed an attempted pull off a Johnson bouncer under the glare of the floodlights.
Mitchell Johnson again proved a thorn in England's side, the left-arm paceman taking one wicket for 20 runs in five overs and twice seeing close lbw decisions against Jonathan Trott overturned in the batsman's favour.