Australia were all but beaten at 91-7, chasing 292 for victory in Mumbai on Tuesday.
But Maxwell snatched victory from the jaws of defeat with a remarkable 201 not out, only the third double hundred in World Cup history.
The all-rounder did, however, have to overturn an lbw decision when given out to spinner Noor Ahmad on 27 and received an greater reprieve when dropped on 33 as Mujeeb Ur Raham floored a simple chance at fine leg.
Maxwell also had to battle against severe cramp in the latter stages of his innings.
This, however, simply encouraged the man appropriately nicknamed the 'Big Show' to deploy his full range of extraordinary range of shots, with the 35-year-old's 128-ball stay featuring 21 fours and 10 sixes.
"I've lived a very charmed life out there," said Maxwell, who had missed Australia's win over England in bizarre circumstances after suffering concussion when falling off a golf buggy.
"I feel shocking," he added. "It was quite hot when we were fielding, I haven't done a whole lot of high intensity exercise in the heat.
"I was lucky to stick it out until the end."
Following a top-order collapse, Maxwell needed an ally and found an ideal partner in Australia captain Pat Cummins, who held firm for 12 not out in an extraordinary unbroken stand of 202.
'Kickstart'
Maxwell, asked what his approach had been when Australia were seven wickets down, replied: "For me, it was to stick to being positive, create bad balls.
"The lbw going over the top was the kickstart I needed," added Maxwell, who came in on a hat-trick delivery from paceman Azmatullah Omarzai.
This was only Maxwell's fourth century in 136 one-day internationals but second of the tournament after he struck the fastest World Cup hundred, off 40 balls, against the Netherlands.
"To make the most of it, be not out with Patty out there at the end (that's what) I'm proud of," insisted Maxwell.
Cummins had the best view of anyone at the Wankhede Stadium as Maxwell ended the match with a six to go to his double century in storybook style.
"I think that's the greatest ODI innings I've ever seen, it's probably the greatest ODI innings ever," Cummins told a post-match news conference.
"It's one of those days where you just go, 'I was there in the stadium the day Glenn Maxwell chased down that total by himself."
Cummins, meanwhile, was confident Maxwell would recover in time for Australia's concluding group game against Bangladesh in Pune on Saturday.
"He was cramping but I think you saw out there how much he loves playing for Australia and do anything to play. So, I'm sure it'll be fine."
Five-times champions Australia have now qualified for the semi-finals with a game to spare after starting the tournament with successive defeats by unbeaten hosts India and South Africa, who have already booked their places in the last four.
"Everyone wrote us off after two losses, we've won six in a row now and I hope that belief passes around our changing rooms," said Maxwell.