Completion of a southern hemisphere sweep of the Rugby World Cup quarter-finals took some unexpected twists and turns before Australia edged Scotland in a dramatic finish at Twickenham to line up a semi-final clash with Argentina.
The Pumas, seen as the least likely to reach the last-four before the weekend, scored four tries in a convincing 43-20 victory over injury-depleted Ireland in Cardiff before the Scots threatened a big upset in London.
Scotland, who had beaten the Wallabies in two of their last three tests, led 16-15 at halftime and 34-32 going into the final minute in a downpour only to lose 35-34 after flyhalf Bernard Foley kicked a controversial penalty at the death.
Both semi-finals will be played at Twickenham next weekend with holders New Zealand taking on South Africa in the other after a Six Nations team failed to reach the last-four for the first time.
Scotland had a second semi-final since 1991 within their grasp but South African referee Craig Joubert would not be swayed in his decision to give Australia the last-gasp penalty in a controversial offside decision at a lineout.
Before that, Australia had scored five tries, two by Drew Mitchell who took his World Cup tally to 14, one short of joint record holders Bryan Habana of South Africa and former All Black Jonah Lomu.
Australian coach Michael Cheika said: "It's a penalty and that's the way it works. You've still got to kick it."