Australia (15) 35
Tries: Ashley-Cooper, Mitchell 2, Hooper, Kurindrani
Conversions: Foley 2
Scotland (16) 34
Tries: Horne, Seymour, Bennett
Conversions: Laidlaw 2
Penalties: Laidlaw 5
Bernard Foley's 79th minute penalty helped Australia book a Rugby World Cup semi-final meeting against Argentina as Scotland were denied a first appearance in the last four for 24 years in cruel and controversial circumstances. Referee Craig Joubert awarded a late offside against Vern Cotter's side from a Scottish line-out, despite as Australian hand seemingly knocking the ball on, to allow the two-time champions to claim a last gasp victory in an extraordinary climax.
Mark Bennett had looked like sending Scotland into a semi-final when he intercepted James Slipper's pass with six minutes left, a victory which would have been their first at Twickenham since 1983. But it was not to be for the Six Nations' wooden spoon side from six months ago.
Peter Horne's try and Greig Laidlaw's metronomic boot had Scotland 16-15 ahead at the break, despite Adam Ashley-Cooper, Drew Mitchell and Michael Hooper going over to keep Australia in touch. The controversial sin-binning of Sean Maitland allowed Michael Cheika's side to seemingly take a grip of the contest as Mitchell and Tevita Kuridrani both scored to extend the lead to eight points.
Laidlaw kicked his fifth penalty to give Scotland hope, and a famous victory was in sight when Bennett went under the posts to leave Australia on their knees. But Joubert award a penalty for an accidental offside, without assessment the television match official, with less than two minutes remaining which Foley, amid the teeming rain, converted with aplomb.
Joubert's conduct throughout the episode, which saw him immediately leave the field upon the full-time whistle, will be heavily scrutinised following an indifferent performance. The result, while it puts Australia into another semi-final at the World Cup, sees some northern hemisphere pride restored by Scotland who produced a performance worthy of the occasion.
The final of the four quarter-final clashes saw Australia take on a Scotland side looking to end the southern hemisphere stronghold on the knock-out stages of the World Cup. Having seen Wales, France and Ireland unceremoniously dumped out of the tournament, Cotter's side were under pressure to restore some respectability to the performance of the Europe's finest.
Ahead of attempts to reach a first semi-final since 1991, the Scots had received a timely boost. Forwards Mike Ross and Jonny Gray had both had their three-week bans for a tip tackle against Samoa overturned on the eve of the game, and were reinstalled to the team without hesitation.
Both players were included in the Scotland pack against a Australia side who themselves were without two crucial players in the form of full-back Israel Folau and number eight David Pocock. The Wallabies may have prevailed from Pool A with four successive wins but having played part of the victory over Wales with 13-men there were no guarantees they would be in peak condition for their eighth straight appearance in the knock-out phase.
Having seen their status as tournament favourites damaged by New Zealand swatting aside France at the Millennium Stadium, Australia were keen to make a statement and after dominating the opening exchanges they took the lead after just nine minutes. Tommy Seymour was dragged out of position by Kuridrani who found Ashley-Cooper who scored his first try of the tournament.
But if the 1991 and 2003 champions thought the opening score would set the foundations for a comfortable afternoon they were to be disappointed. After a brisk move ended with Laidlaw putting Scotland on the board with a penalty, they stormed into the led as Horne picked up from the base of a ruck and went right through the Australian defence.
Laidlaw kicked Scotland eight points ahead with a second penalty as the underdogs maintained their early momentum as even the Australia scrum showed signs of crumbling under the pressure. However, the green and gold continued to pour forward and their relentlessness paid dividends as Mitchell went over in the corner to score his 13th World Cup try to cap a patient move.
A third Laidlaw penalty extended Scotland' led to six but unable to stem the tide from Australia they relinquished their advantage from the final play of the first half. Kane Douglas reigned the ball in from a line-out in the corner and Hooper was the eventual beneficiary.
Scotland were sensing an injustice at the start of the second half after Maitland was yellow carded for what television match official Ben Skeen and referee Joubert felt was a deliberate knock-on, and almost inevitably the numerical advantage told. An Australia scrum led to the ball being fed out to Mitchell who made no mistake to take his career World Cup tally to 14.
The arreas were again reduced when Laidlaw kicked from the floor but the walls appeared be closing in on Scotland when Ashley-Cooper went over in the corner, only for the TMO to highlight a knock-on in a previous ruck. Australia came away from the period of pressure with just a penalty, as Maitland remerged but there was more drama to follow.
Maitland's reintroduction coincided with Scotland grabbing their second try just when they threatened to go under, as Finn Russell charged down Bernard Foley's kick. Will Genia hauled back the fly-half but his offload on the floor found Seymour who went over for his fifth try in as many matches.
An end-to-end contest saw Australia rouse themselves to go within a meter of reestablishing their dominance but Stuart Hogg's fine tackle denied Ashley-Cooper. The two-time world champions were not to be kept at bay for long however as Kuridrani bundled his way through.
To keep themselves in contention heading into dying embers of the games, Laidlaw kicked a fifth penalty to put Scotland within a score. The gamble appeared to have paid off when Bennett collected Slipper's ill-judged pass and went over to send the Twickenham crowd into raptures.
Scotland were 120 seconds from facing Argentina next weekend when Jon Welsh found himself on the wrong side and was penalised despite the hand of Nick Phipps appearing to knock the ball on, a decision which the now partizan crowed took exception to. Foley, after an indifferent performance with the boot and amid universal booing, kicked through the posts to complete the southern hemisphere clean sweep.
Australia: 15. Kurtley Beale, 14. Adam Ashley-Cooper, 13. Tevita Kuridrani, 12. Matt Giteau, 11. Drew Mitchell, 10. Bernard Foley, 9. Will Genia; 1. Scott Sio, 2. Stephen Moore, 3. Sekope Kepu, 4. Kane Douglas, 5. Rob Simmons, 6. Scott Fardy, 7. Michael Hooper, 8. Ben McCalman.
Replacements: 16. Tatafu Polota-Nau, 17. James Slipper, 18. Greg Holmes, 19. Dean Mumm, 20. Sean McMahon, 21. Nick Phipps, 22. Matt Toomua, 23. Quade Cooper.
Scotland: 15. Stuart Hogg 14. Sean Maitland 13. Mark Bennett 12. Peter Horne 11. Tommy Seymour 10. Finn Russell 9. Greig Laidlaw; 1. Alasdair Dickinson 2. Fraser Brown 3. WP Nel 4. Tim Swinson 5. Richie Gray 6. Blair Cowan 7. John Hardie 8. Dave Denton
Replacements: 16. Kevin Bryce 17. Gordon Reid 18. Jon Welsh 19. Alasdair Strokosch 20. Josh Strauss 21. Henry Pyrgos 22. Richie Vernon 23. Sean Maitland.