Australia 33-16 Scotland
Defending champions Australia shrugged off a poor first-half performance to book their place in the semi-finals.
When the teams turned round level at 9-9 it looked as though the lacklustre Wallabies were going to be pushed all the way by a revitalised Scotland.
However, Australia raised their game after the break and once Stirling Mortlock cruised over six minutes into the half there was only going to be one winner.
Captain George Gregan and David Lyons added further tries for the Wallabies, who will now play bitter rivals New Zealand for a place in the World Cup final.
From the outset Australia were determined to get the ball wide and use their dangerous strike runners on the wings.
Lote Tuqiri looked especially threatening with the ball in hand but he was not seeing as much of it as he would have liked because the Australians were struggling to secure decent possession.
The Scots were disrupting them at the scrum and the lineout and Australia looked most threatening when they turned over Scottish ball.
A penalty apiece from Flatley and Paterson saw the sides locked together at 3-3 after 10 minutes and it was nip and tuck for the rest of the half.
Two Flatley penalties to one from Paterson saw the Wallabies leading 9-6 before the Scotland fly-half ensured it was all square at the break.
Paterson had been hit in the face by a ball before kick-off but he showed no ill effects when he let fly with a monster drop goal to make it 9-9.
It could have been better for the Scots, who were denied a possible try-scoring opportunity by referee Steve Walsh.
The referee, who also failed to pick up a number of blatant obstructions, did not allow any advantage as Kenny Logan chased a threatening Gregor Townsend kick.
Australia took off George Smith and brought on the 6ft 5in Matt Cockbain to boost their lineout for the second half and they were soon handed a lucky break.
Phil Waugh was ruled on-side when he turned over the ball and once Stirling Mortlock had blasted through Glenn Metcalfe's flimsy tackle he was left with an easy run to the line.
Flatley converted and added a penalty to give Australia a 19-9 lead with half an hour to play, before Gregan kicked through and touched down under the posts.
David Lyons added a third try for Australia and, with Flatley adding both conversions, Australia had a healthy 33-9 lead, making Robbie Russell's late converted try no more than a consolation for the Scots.
Despite the 17-point margin of victory Australia still look short of their best and they know they will have to exert a lot more control up front if they are to beat the All Blacks when they meet in the last four next weekend.
Australia: M Rogers; W Sailor, S Mortlock, E Flatley, L Tuqiri; S Larkham, G Gregan (capt); B Young, B Cannon, B Darwin, J Harrison, N Sharpe; G Smith, P Waugh, D Lyons.
Replacements: J Paul, A Baxter, D Vickerman, M Cockbain, C Whitaker, M Giteau, J Roff.
Scotland: G Metcalfe, S Danielli, G Townsend, A Henderson, K Logan, C Paterson, B Redpath (capt), T Smith, G Bulloch, B Douglas, N Hines, S Grimes, J White, C Mather, S Taylor.
Replacements: R Russell, G McIlwham, S Murray, J Petrie, M Blair, J McLaren, B Hinshelwood.
Referee: Steve Walsh