Australia have booked their place in the semi-finals of the 2015 Rugby World Cup courtesy of a thrilling 35-34 victory over Scotland at Twickenham this afternoon.

A gripping contest swung both ways throughout the 80 minutes, but ultimately it was a last-minute penalty from Bernard Foley that set up a last-four showdown with Argentina.

Australia went into the match as heavy favourites despite losing two of the last three meetings between the sides, and it was they who made a storming start with early possession deep in the Scotland 22.

One chance went begging when Drew Mitchell knocked on just yards from the line following Foley's mini-break, but the Wallabies soon crossed over for the opening try of the contest when Tevita Kuridrani set up Adam Ashley-Cooper to score on his 112th cap.

That tally makes him the third-most capped Australian player ever, and with captain Stephen Moore and centre Matt Giteau joining him in the centurion club this afternoon, they soon needed to call on every bit of that experience as Scotland began to turn the tide.

A Greig Laidlaw penalty got Vern Cotter's side on the board from their first meaningful attack, and they were quickly back on the offensive having been forced to weather an ominous storm in the opening 10 minutes.

Again they moved into the Australian 22, and this time they breached a defence that had proved so resilient against Wales last time out when Peter Horne darted over from the base of a scrum.

It should have been even better for the Scots shortly after another successful Laidlaw penalty when Kuridrani gifted the ball to Finn Russell when looking to offload, only for Russell's pass to be dropped by Mark Bennett with clear grass in front of him.

Michael Cheika's side looked rattled, but they soon composed themselves and began to build some momentum of their own, which resulted in Mitchell going over in the corner after some patient build-up play.

For the second time in the match, Foley was unable to convert from the touchline, and his uncharacteristic misses continued to be punished by Laidlaw, who kicked his third penalty of the match to extend the lead to six points.

That would be cut to one by half time courtesy of an attacking move from captain Moore, who opted to kick for touch instead of going for goal. It proved to be a good decision when Michael Hooper touched down from the resulting driving maul, but once again Foley was unable to add the extras.

Scotland were dealt a big blow in the opening stages of the second half when Sean Maitland was sent to the sin bin for a deliberate knock-on, and Australia immediately made the most of their numerical advantage when Mitchell went over for his second of the game and 14th at a World Cup, putting him behind only Jonah Lomu and Bryan Habana in the all-time list.

This time Foley did convert, but Scotland quickly pegged the Wallabies back through another Laidlaw penalty.

As it turned out, Australia only managed seven points during Maitland's time off the field, but they thought they had added a fifth try of the match before his re-introduction when Ashley-Cooper finished off a move in the corner, only for the TMO to rule that there had been a knock-on in a ruck during the build-up.

After a shaky first half from the tee, Foley made it two from two in the second with a penalty, but the fly-half then saw an attempted chip blocked and collected by Russell, who managed to offload for Tommy Seymour to score Scotland's second try of the match.

That reduced the deficit back to one, but Laidlaw was unable to edge his side back in front when his kick from the touchline was unsuccessful, and that in turn allowed Australia to move two scores ahead when Kuridrani burrowed over from close range after Scotland had lost a lineout on their own throw inside the 22.

A fifth Laidlaw penalty brought Scotland back within range, and as the rain began to fall at Twickenham they created another twist in the tale when Bennett intercepted a pass and ran in unchallenged under the post to draw his side level.

Laidlaw's conversion then put Cotter's side back in front, but Australia were handed a late penalty which Foley converted to give his side a dramatic one-point victory.

The result means that there will be no Northern Hemisphere teams in the semi-finals of the World Cup for the first time ever.