The Wallabies have outlasted Argentina 29-15 in a tense Rugby World Cup semi-final to set up a mouth-watering final with arch-rivals New Zealand.

Adam Ashley-Cooper scored a hat-trick of tries against the Pumas, who were gallant throughout the contest.

Worrying coach Michael Cheika will be a suspected flare up of an ankle injury to star fullback Israel Folau, who left the field midway through the second half of the bruising encounter at Twickenham on Sunday (Monday AEDT).

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Ashley-Cooper sealed the win, and Australia’s spot in a fourth World Cup final, with his third try with eight minutes remaining, when he cashed in on a brilliant run by fellow winger Drew Mitchell.

Drew Mitchell makes the break that led to Ashley-Cooper’s sealer. Photo: Getty

Mitchell beat six Pumas defenders on a sensational winding, cross-field run before linking up with Ashley-Cooper who crossed out wide to kill off Argentina’s hopes of a maiden World Cup final.

But it was far from the complete performance by Australia, with an enterprising Argentina regularly finding half-breaks – but as they have done throughout the World Cup, the Wallabies allowed their defensive line to bend but not break and their tryline was not breached.

The Wallabies shot out of the blocks and had two tries inside the first 10 minutes, but the explosive start belied the exhausting contest which was to follow.

The first had a touch of luck – with giant second-rower Rob Simmons snatching an intercept from Pumas No.10 Nicolas Sanchez to race away and score under the posts in the second minute.

Seven minutes later Bernard Foley took a leaf out of the playbook of attack coach Stephen Larkham to throw a superb cut-off pass which hit the chest of Ashley-Cooper.

The veteran made no mistake, and scampered to the corner to put Argentina right on the back foot just ten minutes into the game.

Ashley-Cooper had his second, on the other side of the field, from a similarly pinpoint cut-out ball by Matt Giteau which gave Australia a 19-9 halftime advantage.

Argentine football legend Diego Maradona watches on at Twickenham. Photo: Getty

Sanchez booted five penalties to have all 15 points for Argentina, who were reduced to 14 men in the first half following the sin-binning of lock Tomas Levantine for a no-arms tackle on Folau.

Folau, who overcame an ankle injury which ruled him out of last weekend’s quarter-final win over Scotland, was jittery under the high-ball and made some questionable kicks – but again recovered with incisive runs to make an impact before being replaced with 15 minutes remaining.

The return of champion back-rower David Pocock from a calf injury had an immediate impact on the Wallabies controlling the breakdown – he had two turnovers in the opening 20 minutes and finished with three, taking his tournament tally to 13.

Pocock played the entire 80 minutes to dispel fears over his injury and remains Australia’s best hope of securing an upset over the defending champion All Blacks at Twickenham on Saturday.

The unsung hero of Australia’s all-star back row, No.6 Scott Fardy, was also outstanding – topping the tackle count with 16 and crucially shutting down an Argentinian attacking raid late in the second half when an overlap was looming.

The Australian scrum, missing starting loosehead prop Scott Sio who was sidelined with an elbow injury, was unrecognisable from the dismantling of England during the pool stages.

Replacement No.1 James Slipper conceded three scrum penalties before being replaced early in the second half as Argentina dominated in an area the All Blacks will look to target next week.

The World Cup final will kick off at 3am (AEDT) next Sunday morning.