The veteran all-rounder defied an injury that left him essentially batting on one leg to hit a stunning double century and rescue his side from seven wickets down for just 97 runs to beat Afghanistan by three wickets in a Mumbai classic on Tuesday.
Maxwell, who suffered from back spasms and cramp throughout his incredible knock, struck a truly remarkable 201 off 128 balls that included 10 sixes and 21 fours as Pat Cummins' side successfully chased down a target of 292.
It was with the last of those sixes that the 35-year-old - who battled on despite appearing in some pain - wrapped up the win with 19 deliveries to go.
"Just ridiculous!" Cummins said afterwards. "It's got to be the greatest ODI innings that's ever happened, it's one of those days where you just go, 'When that happened, I was here in the stadium'."
It was the highest-ever score by an Australian in a one-day international, as the team achieved the highest successful ODI run chase there had ever been at the Wankhede Stadium.
The ground had seen history made earlier with Afghanistan recording their maiden World Cup century, Ibrahim Zadran posting an unbeaten 12.
Their total of 291 for five also featured contributions of 35 not out from Rashid Khan and 30 from Rahmat Shah as Afghanistan sought to beat Australia for the first time at the fourth attempt in this format.
Australia's reply started badly with Travis Head being dismissed for a duck by Naveen-ul-Haq with only four runs on the board.
And the wickets continued to go as Cummins' men stumbled to 49 for four after Azmatullah Omarzai took the scalps of David Warner and Josh Inglis in consecutive balls.
When Mitchell Starc was ousted - despite questions over whether the ball had hit his bat - via a superb catch from wicketkeeper Ikram Alikhil to leave Australia at 91 for seven in the 19th over, Afghanistan looked to be closing in on a famous victory.
But Maxwell then took centre stage with a stunning display to push Australia to victory.
Having been dropped and survived an lbw appeal on review, he went on to register boundary after boundary, even though at times he looked to be in considerable discomfort and struggling to run.
Able to continue after receiving treatment on the field, he subsequently completed his double-century - and Australia's win - in fitting fashion by crashing yet another maximum that took his partnership with Cummins (12) to 202.
Third-placed Australia advance into the last four, joining India and South Africa, ahead of finishing their group matches by playing Bangladesh in Pune on Saturday.
Afghanistan remain sixth, with one of them, New Zealand and Pakistan set to make the semi-finals - they face South Africa in Ahmedabad on Friday.
Additional reporting by the Press Association.