Australia recovered from a shaky start to score 294 for nine in their 50 overs and while Sam Billings struck an impressive maiden ODI century, the hosts were always behind the game.
“It was nice to win and start off the series really well,” Australia captain Aaron Finch said.
“It was a great partnership. They paced it really well. They played two really smart, mature innings and I’m really happy for them two to get some runs.”
England put the visitors in and had them reeling on 123 for five but Marsh (73) Maxwell (77) helped Australia rebuild on their way to a formidable total.
After slumping to 57-4 in reply and falling way behind the required run rate it looked bleak for England but Jonny Bairstow and Billings shared a century stand for the fifth wicket to edge Eoin Morgan’s side back into contention.
Bairstow was caught slogging off spinner Adam Zampa and when Moeen Ali became Josh Hazelwood’s third wicket soon after Australia could breathe a little easier.
An inspired Zampa picked up his fourth wicket when Chris Woakes was caught by Maxwell but Billings refused to give up on what would have been the highest ODI run chase at Old Trafford.
England required 66 from the last six overs but Australia, beaten comfortably by England in the World Cup semi-final last year, locked up a morale-boosting victory having lost the T20 series 2-1.
Billings was out on the last ball of the innings for 118 as England finished on 275-9.
“The game probably slipped away from us in the first 10 to 12 overs with the bat,” England skipper Morgan said. “We thought we could chase it down if we established a few partnerships. I thought they played well.”