Glenn Maxwell fought through cramps to smash an unbeaten 201 off 128 balls, single-handedly guiding Australia to an improbable three-wicket win over Afghanistan in a World Cup match on Tuesday and sealing the team's spot in the semi-finals.

Afghanistan appeared set for a famous victory against five-time champions Australia at the floodlit Wankhede Stadium, reducing them to 91 for seven wickets after setting them a victory target of 292.

But the Afghans then watched in disbelief as Maxwell launched an extraordinary counter-attack. With captain Pat Cummins for company, Maxwell took Australia past Afghanistan's total of 291 for five wickets with 19 balls to spare.

The right-handed batsman suffered cramps after going past his fourth hundred in the 50-over format but laboured on, cutting down on running between the wickets to manage the pain and relying more on big hits.

In total, Maxwell hit 21 fours and 10 sixes during his knock - many of them on one leg and the last six sealed the victory and also brought up his double century.

"Horrific, I feel shocking," said Maxwell. "It was quite hot when we were fielding, I haven't done a whole lot of high intensity exercise in the heat. It got a hold of me today, I was lucky to stick it out until the end."

Cummins remained unbeaten on 12 from 68 balls but more importantly added 202 for the unbroken eighth wicket partnership.

Afghanistan held numerous meetings on the ground but were unable to find a way to dislodge Maxwell, who was dropped on 33 by Mujeeb Ur Rahman off Noor Ahmad's bowling.

Maxwell was also adjudged out leg before wicket in the same over against Noor but the batsman managed to successfully overturn the umpire's decision on appeal.

"Really disappointed. Cricket is a funny game, it was unbelievable," Afghanistan captain Hashmatullah Shahidi said.

"We were in the game. Our bowlers started really well, we dropped chances for the eighth wicket. Maxwell doesn't stop, I have to give credit to him."

Afghanistan seamers Naveen-ul-Haq and Azmatullah Omarzai had struck early blows with the ball to reduce Australia to 49-4 after opening batsman Ibrahim Zadran's maiden World Cup hundred helped Afghanistan post a competitive total.

With Steve Smith missing from the side due to a bout of vertigo, Australia did not seem to have the batting depth to chase down the target and Rashid Khan's two quick strikes seemed to have all but sealed the match in Afghanistan's favour.

Tuesday's victory took Australia to 12 points. They became the third team to reach the semi-finals with India and South Africa having already booked their spots.

Zadran anchored the Afghan innings earlier with an unbeaten 129 from 143 balls after the South Asian side won the toss and elected to bat. The 21-year-old Zadran's fifth hundred in the 50-overs format was studded with eight fours and three sixes.

All-rounder Rashid smashed an unbeaten 35 off 18 balls with three sixes and two fours to provide Afghanistan with some quick runs towards the end.