Australia ran in four tries as they overcame a brave challenge from Scotland at Hampden Park.
Scotland were effective in the set piece and Chris Cusiter enjoyed a fine game for them at scrum-half.
But they lacked the cutting edge of the tourists, who grabbed tries through Lote Tuqiri, David Lyons, Matt Giteau and their captain George Gregan.
Alistair Hogg, charging down a kick from Australian substitute Elton Flatley, claimed Scotland's only try.
The Scots, buoyed by last week's record 100-8 win over Japan, started strongly.
They were in control at the lineout and briefly led 6-3 thanks to penalties from Sydney-born fly-half Dan Parks and Chris Paterson.
But Australia, who came into the game on the back of a 27-14 defeat by France, gradually took control.
And in the 22nd minute the ever-dangerous Tuqiri went over for his sixth try in four matches against Scotland.
The score was controversial though, as George Smith appeared to knock on early in the move leading to the try.
The visitors possessed the cunning the Scots were so patently lacking and went further ahead when back-row forward Phil Waugh held off a weak Sean Lamont tackle to go over.
Scotland closed to within five points early in the second half courtesy of another Paterson penalty.
But any hopes they had of beating their visitors at Hampden Park for the first time since 1982 ended when Giteau ghosted between Scotland's centres for another Australia try.
Hogg did restore some pride for the Scots with his late effort.
He charged down a kick from Flatley 15 yards out from the Australia line and evaded Giteau to score.
But Australia skipper George Gregan finished a slick move in the dying minutes to restore his side's advantage.
Scotland: H Southwell, C Paterson, B Hinshelwood, A Henderson, S Lamont, D Parks, C Cusiter, A Jacobsen, G Bulloch (capt), G Kerr, S Grimes, N Hines, A Hogg, J Petrie, D Macfadyen.
Replacements: R Russell, B Douglas, S MacLeod, J White, M Blair, G Ross, G Morrison.
Australia: C Latham, C Rathbone, S Mortlock, M Giteau, L Tuqiri, S Larkham, G Gregan (capt), D Lyons, P Waugh, G Smith, D Vickerman, J Harrison, A Baxter, J Paul, B Young.
Replacements: B Cannon, M Dunning, R Samo, S Hoiles, E Flatley, W Sailor, M Rogers.