Match report and highlights: Australia 35-34 Scotland
Scotland were denied a place in the World Cup semi-finals when Australia snatched a dramatic 35-34 victory with only seconds to spare at Twickenham.
Fly-half Bernard Foley landed a routine penalty in the 80th minute after the Scots had fought back to lead 34-32 when centre Mark Bennett scored an intercept try.
For the first time in World Cup history there will no Six Nations team in the semi-finals after Argentina thrashed Ireland earlier in the day. Australia will face Argentina on Sunday.
Scotland offered Europe their last hope of avoiding a chastening southern hemisphere clean sweep in the World Cup semi-finals when they faced Australia at Twickenham.
Hooker Ross Ford and lock Jonny Gray were restored to the starting XV shortly before kick-off after the appeals into their three-match suspensions were upheld.
Australia had lost back row David Pocock and full-back Israel Folau to injury, but openside Michael Hooper was back from suspension.
Australia threatened the whitewash inside the opening five minutes after inching upfield with a succession of carries. Fly-half Bernard Foley almost wriggled over and when he was tackled his pass to Drew Mitchell was forward.
Scotland only had themselves to blame when their line was breached in the ninth minute after wing Tommy Seymour shot forward in search of a big hit on Tevita Kuridrani only for the muscular Wallabies centre to casually shrug him off.
A gap had appeared before Kuridrani and he raced forward before sending Adam Ashley-Cooper over.
Greig Laidlaw's penalty rewarded a promising spell of Scottish play but there was better to come as they conjured an 18th minute try, patiently battering away at the Wallabies' defence until an enormous hole opened up at the breakdown and centre Peter Horne seized his chance.
A mighty roar greeted the sight of Foley dropping a high ball when under no pressure and Twickenham sensed an upset was possible.
Finn Russell robbed the ball from Kuridrani and fed Mark Bennett only for the centre to drop the pass, but he made amends with a crucial tackle on Matt Giteau shortly after.
There was an inevitability about Australia's second try as Scotland's defence became over-stretched in the face of a Wallabies onslaught and a long pass by Beale sent Drew Mitchell over.
A second penalty by Laidlaw pushed Vern Cotter's men six points ahead and another rousing passage of play renewed hope of Six Nations representation in the semi-finals.
Australia's ambition with a minute of the first half remaining paid off, however, when a penalty that offered an easy three points was kicked into touch and from the resulting line-out drive Hooper was shoved over.
INTRO: Scotland sensed a stunning World Cup upset was possible after claiming a one-point lead at half-time of their quarter-final against Australia at Twickenham.
Centre Peter Horne crossed in the 18th minute and scrum-half Greig Laidlaw kicked the conversion and three penalties.
Australia scored tries through Adam Ashley-Cooper, Drew Mitchell and Michael Hooper to keep them in touch.
Scotland could not have endured a worse possible start to the second half as wing Sean Maitland was harshly sent to the sin-bin by referee Craig Joubert for a deliberate knock-on - it appeared accidental - before their line cracked again.
A line-out drive did the damage once more but this time the ball was released with Will Genia sending Mitchell over for his second try.
Scotland replied with a Laidlaw penalty and were relieved to see an Ashley-Cooper try chalked off for a knock-on by Genia.
A frantic passage of play followed with Australia conceding ground down the right wing and once the game had resumed after a scrum, Russell charged down a kick by Foley for Seymour to gather over the line and score.
Australia led just 25-24 as the final quarter arrived and when Kuridrani used his might to force his way over from short range, there was daylight between the teams.
Laidlaw slotted a penalty as rain began to fall at Twickenham and a nail-biting final six minutes were ensured when Bennett intercepted a pass by replacement prop James Slipper to dive over under the posts with Laidlaw converting.
A scrum free-kick nudged Scotland ever closer to a remarkable win but disaster struck with a minute remaining when Joubert signaled a penalty for offside and a nerveless Foley was on target to spark Australian victory celebrations.