Australia skipper Pat Cummins hailed Glenn Maxwell's epic World Cup double century as the "greatest innings" on Tuesday as the swashbuckling batsman defied injury to spark a three-wicket win over Afghanistan.

Maxwell made 201 not out off 128 balls with 21 fours and 10 sixes as five-time champions Australia recovered from 91-7 to chase down their 292-run target.

"Just ridiculous. I don't know how you describe that," said Cummins.

"A great win but Maxi was just out of this world. It's got to be the greatest ODI innings that has ever happened."

Cummins played a supporting role with an undefeated 12 off 68 balls as Australia made the semi-finals.

"It's one of those days where you can just think, 'yep, when that happened I was there in the stadium' and feel very lucky," added Cummins.

Maxwell rode his luck, he was dropped on 33 and overcame cramps to see his team home. He also used a review to overturn an lbw decision against him early in his innings.

He came into the game having missed the last match against England having suffered a concussion after falling off the back of a golf buggy.

"Horrific, I feel shocking. It was quite hot when we were fielding, I haven't done a whole lot of high intensity exercise in the heat," said Maxwell.

"It got a hold of me today, I was lucky to stick it out until the end."

Maxwell, nicknamed the 'Big Show', has been in fine form at the tournament, hitting a record 40-ball century earlier in the World Cup.

"It would've been nice if it was chanceless, I've lived a very charmed life out there," he added.

"To make the most of it, be not out with Patty out there at the end I'm proud of."

Afghanistan skipper Hashmatullah Shahidi was stunned by the turn of events.

"Really disappointed. Cricket is a funny game, it was unbelievable," he said.