Chasing 303, the tourists looked dead and buried at 5-73 - the lowest score Australia's fifth wicket has fallen in an ODI against England since 1977 - when Maxwell joined Carey at the crease.

Maxwell, often maligned for not producing when Australia need it most, had a day to remember as he smashed seven sixes and four boundaries in his 108 from 90 balls as the world champions suffered a first home series defeat in five years.

Carey, 106, also found form when it mattered with his maiden international century as the duo chalked up the highest sixth-wicket partnership of all-time in one-day internationals before Maxwell fell to Adil Rashid 18 runs shy of victory.

The South Australian fell to the final ball of the penultimate over from Jofra Archer when Mark Wood took a fantastic diving catch in the deep.

It required pace duo Mitchell Starc and Pat Cummins to get Australia home with 10 runs needed from the final over bowled by Adil Rashid.

Starc hit the first delivery for six and then the third ball for four to seal a memorable win with two balls to spare.

Maxwell also became the become the fastest man to score 3000 ODI runs as Australia buried the memory of Sunday's meltdown in the second match of the series.

"Maxy is in the team to do a specific role, and that's to be able to take the game away from opposition but also be that guy to counterattack and swing momentum in changing rooms," captain Aaron Finch said.

"What makes him so damaging is he can play all around the ground.

"I don't think there's many bowlers in the world that can trouble him when he is having one of those days.

"The way he navigated that innings and took it deeper and deeper ... he did that perfectly."

The turning point of the match happened in the 20th over when Jofra Archer thought he had Carey caught at third man for nine, only for video review to show he had overstepped the mark to deliver the first no ball of his ODI career.

Buoyed by that reprieve at 5-95, the pair set about rebuilding the tourists' innings and then stepped up a gear to attack the English attack in the final 25 overs.

England had earlier recovered from being 0-2 after the first two balls of the match, bowled by Starc to score 7-302 thanks to Jonny Bairstow's 112 and 57 from Sam Billings and Chris Woakes' unbeaten 53.

Australia's response started terribly when Finch fell lbw in the third over to Woakes for just six.

He was joined back in the pavilion soon after by Marcus Stoinis, whose difficult series continued when he was deceived by a slower ball from Woakes and lobbed an easy catch to Eoin Morgan for four.

Morgan has become accustomed to being on the right side of things in the 50-over format but felt a setback on challenging wickets at Old Trafford was a more instructive experience than walkovers on perfect batting tracks.

"The positive of the series is knowing we can win games of cricket when we don't play our best game," he said.

"I know we've not played our best but the character and resilience we've showed has been brilliant."

Australian Associated Press