The twice winners were only fifth favourites before the start of the tournament but underlined their credentials with impressive wins over England and Wales in the so-called "pool of death".
Australia start as hot favourites to overcome Scotland, back in the knockout stage after missing out four years ago, but coach Michael Cheika believes Vern Cotter's side will pose the Wallabies their toughest test so far.
"This will be the most difficult game we play and that’s not disrespecting our other opponents at all because every match has been tough, but this will be the toughest," he said.
"There’s going to be a lot of pain, it’s going to be physical and I want the players to enjoy that as well because that’s when it’s worth it.”
Australia's much-maligned scrum has improved considerably under the guidance of former Argentina international Mario Ledesma, but the flourishing halfback pairing of Will Genia and Bernard Foley that has also caught the eye.
EFFECTIVE COMBINATION
Flyhalf Foley masterminded the win over England with two tries and 18 points from his boot and he and Genia are proving an increasingly effective combination.
"I think it’s still growing, we’ve still got a fair bit to improve on and I think we can take it to another level for sure," Foley said of their partnership.
Victories for Scotland against the southern hemisphere's major sides are not quite as rare as recent wins at Twickenham -- their last success at the home of English rugby came in 1983 -- but they can point to two wins from their past three meetings with Australia as reason for optimism.
"They haven’t lost a game yet, so they are the form team and the favourites not only to beat us but to go on and win the World Cup," Scotland coach Cotter said. "They are a team that is more dangerous at the end, so we can't even allow a slight slip in concentration."
Cotter's men could do no worse than conjure the spirit of 2012, when on a filthy night at the Hunter Stadium in Newcastle, New South Wales, with the rain pouring and the wind howling, Scotland produced a heroic performance in defence.
With the game level at 6-6 in added time, Greig Laidlaw stepped up to nail a penalty to secure a memorable victory.
Both sides have been forced into making changes. Australia will be without influential flanker David Pocock and fullback Israel Folau through injury, while Scotland have lost forwards Ross Ford and Jonny Gray to suspension.
Teams:
Australia: 1-Scott Sio, 2-Stephen Moore (captain), 3-Sekope Kepu, 4-Kane Douglas, 5-Rob Simmons, 6-Scott Fardy, 7-Michael Hooper, 8-Ben McCalman; 9-Will Genia, 10-Bernard Foley, 11-Drew Mitchell, 12-Matt Giteau, 13-Tevita Kuridrani, 14-Adam Ashley-Cooper, 15-Kurtley Beale
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: 1-Alasdair Dickinson, 2-Fraser Brown, 3-WP Nel, 4-Tim Swinson, 5-Richie Gray, 6-Blair Cowan, 7-John Hardie, 8-Dave Denton; 9-Greig Laidlaw (captain), 10-Finn Russell, 11-Tommy Seymour, 12-Pete Horne, 13-Mark Bennett, 14-Sean Maitland
15-Stuart Hogg.
Replacements: 16-Kevin Bryce, 17-Gordon Reid, 18-Jon Welsh, 19-Alasdair Strokosch, 20-Josh Strauss, 21-Henry Pyrgos, 22-Richie Vernon, 23-Sean Lamont.
Referee: Craig Joubert (South Africa)
(Editing by David Goodman)
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