Glenn Maxwell and Mitchell Marsh each registered 70s with the bat before Josh Hazlewood and Adam Zampa took seven wickets between them to seal the win despite a maiden ODI century from Sam Billings.
Returning to the side having missed the final T20I with a dislocated finger, England captain Eoin Morgan won the toss and elected to bowl first.
Jofra Archer produced a peach of a delivery to take the top of David Warner's off stump to provide England with an early breakthrough. Aaron Finch also fell within the first Powerplay, nicking off to Mark Wood's first delivery.
Marcus Stoinis, batting at three in the absence of Steve Smith who was left out as a precautionary measure after taking a blow to the head while training on Thursday, raced to 43 before he fell in a similar fashion to his captain to the same bowler.
Marnus Labuschagne and Alex Carey both fell to Adil Rashid, who has now claimed eight wickets across four matches against Australia this year, before Marsh and Maxwell came together.
By the time Archer removed Maxwell, the all-rounder had already racked up 77 runs from 59 balls and the pair had more than doubled the score, from 123/5 to 249/6. Wood trapped Marsh in front before he was able to really tee off at the death, but Mitchell Starc's innings, including a last-ball maximum, lifted the total to 294/9.
Chasing what would have been a record chase at Old Trafford in ODIs, England's reply quickly fell into trouble as Josh Hazlewood claimed the wickets of Jason Roy and Joe Root to reduce the host to 13/2 after 7.1 overs.
Morgan managed to get the innings moving with a brisk 23 before he fell to Adam Zampa, who then had Jos Buttler caught in his next over to leave England again needing to rebuild.
Jonny Bairstow combined with Sam Billings and after a period in which both batsmen struggled to find their timing, the opener got going with a pair of sixes off Zampa. But it was also the leg-spinner who put an end to Bairstow's charge after 84 runs and 107 balls.
Billings took the lead then, and kept England in with an outside chance even as wickets tumbled at the other end. The Kent batsman reached his maiden ODI century but was unable to keep up with the rate, and eventually fell for 118 from the final ball of the innings as Australia sealed a 19-run victory.
The result means that Australia have registered their first points in the ICC Men's Cricket World Cup Super League from their first match in the tournament, moving equal with Ireland on 10 points.
The second ODI will be played on Sunday, 13 September, at the same venue.