An injury-hit Australia fell just short of claiming a tremendous backs-to-the-wall victory against South Africa at the Cricket World Cup on Sunday morning (AEST).

Chasing 326 for victory, Australia was 4-119 in the 25th over and looked no chance.

But David Warner (122) and Alex Carey (83) batted superbly at Old Trafford, giving Australia a sniff of victory.

Both batsmen fell as the run-rate steadily climbed, though, leaving the tail with too much to do as Australia was eventually bowled out for 315 with one ball remaining.

Defeat means Australia finishes second on the World Cup standings, one point below India, meaning Aaron Finch’s side will play England in a semi-final on Thursday.

India will play New Zealand in the other semi-final to be held on Tuesday.

South Africa, with no chance of making the semi-finals, set Australia an imposing chase, as Faf du Plessis hit 100 in a score of 6-325.

Mitchell Starc (2-59) was far from his best but his two wickets saw him equal Glenn McGrath (26) as the highest Australian wicket-taker in one World Cup tournament.

Starc (knee) was one of three Australia players to seemingly battle injury, too, as Usman Khawaja was forced to initially retire hurt with a hamstring problem before returning to the crease in the dying stages.

Marcus Stoinis also appeared to battle with a side strain during his innings and bowled just three overs.

The injuries are coming at the wrong time for Australia, with Shaun Marsh ruled out of the tournament after fracturing his arm in a Thursday training session.

Australia captain Finch said after the match that the side failed to bowl at its best.

“We didn’t really hit our areas consistently enough [with the ball]. It’s obviously a little bit frustrating but I think it’s also a time when we can learn from it, as well,” he said.

“A real positive is, like I said, we still managed to get really close while not playing our best cricket.”

Finch added that Khawaja’s injury situation “doesn’t look ideal” and that he will have scans on his hamstring in the next 24 hours, but that he was “not sure” about the severity of Stoinis’ problem.

Turning his attention to the England match, Finch added: “It’s going to be a blockbuster. It doesn’t get much bigger than that, Australia England in a World Cup semi-final. Hopefully it will be a great game.”

Australia should have lost a wicket just three balls into its chase, but a throw to the wrong end cost South Africa a likely run out.

Finch spooned a catch to Aidan Markram in the third over, though, falling for just three to Imran Tahir (1-59) in his last one-day international.

Khawaja twice called for the physio and was initially forced to call it quits just five balls into his innings and then, after another near run-out, Steve Smith (7) was trapped lbw by Dwaine Pretorius (2-27).

Stoinis did not score from the first 13 deliveries he faced, heaping the pressure on Warner, but the left-hander produced regular boundaries to keep Australia in the hunt.

Stoinis was then run out for 22 before a brilliant Quinton de Kock catch saw Glenn Maxwell caught behind for 12.

Warner and Carey changed the course of the game with a 108-run partnership in just 15 overs but just as Australia started to threaten, Warner – who hit 15 fours and two sixes – was superbly caught by Chris Morris.

Carey stepped up in Warner’s absence, and raced to 83 off just 66 deliveries. His wicket, in the 46th over, proved crucial, the wicket-keeper picking out Markram at deep extra cover, a scalp that saw Khawaja (18) return to the crease.

He and Starc (16) chipped in with some boundaries, but both were bowled by Kagiso Rabada (3-56), with Nathan Lyon the last man to fall for three.

Earlier, Markram (34) and de Kock (52) gave South Africa a brilliant start.

The pair added 73 runs in the first 10 overs, targeting the Australia attack no matter who was the bowler.

Markram set the tone with two fours in the first over from Starc and after racing to 32, he was dropped by Jason Behrendorff (1-55) off his own bowling.

It did not cost Australia, though, Markram falling shortly after, stumped by Carey off the bowling of Lyon.

Lyon (2-53) was clearly Australia’s best bowler, adding the scalp of De Kock when he picked out Starc at backward point.

But that brought Du Plessis and Rassie van der Dussen (95) together and they combined for a 151-run partnership that set the platform for South Africa’s big score.

Van der Dussen could have been stumped on five, but Carey misread a Maxwell (0-57) delivery, and the batsman made Australia pay.

He really stepped up once du Plessis fell in the same over in which he reached his 12th one-day international century, slogging hard in the final overs before falling five runs short of a hundred when he holed out to Maxwell off the last ball of the innings.

Starc chipped in with two late wickets but South Africa already had a big score on the board, one that would ultimately prove too much.