The Wallabies were forced into an early substitution when centre Stirling Mortlock was forced off - with a suspected broken cheekbone - to be replaced former league star Wendell Sailor.
The change did not affect the visitors' momentum and from a scrum inside the Scotland half the home side were penalised and Matt Giteau put the Wallabies ahead in the ninth minute.
Scotland hit back immediately when George Smith was adjudged offside and then the Wallabies infringed at a line-out, Chris Paterson slotting both straightforward penalties.
The Wallabies scored the opening try on 21 minutes when another former league man Lote Tuqiri went in at the corner following a slick handling move in the visiting backs, Giteau converting.
Tuqiri was penalised for holding on soon after though and Paterson made no mistake with the kick.
But Phil Waugh soon notched his fourth try in the green and gold after Scotland's defence was stretched to breaking point.
Giteau converted to leave the score 17-9 with half-time looming.
The Wallabies' third league convert Mat Rogers came on just before the interval in place of Clyde Rathbone while Elton Flatley filled in for Stephen Larkham in a blood substitution which became permanent at half-time.
After Scotland's best period of pressure in the game, Australia struck back to regain a comfortable lead when Giteau crossed after the Scotland defence was stretched by a mazy run from hooker Jeremy Paul.
The Scots refused to lie down though and seconds later Flatley's kick was charged down by Hogg, who gathered brilliantly and charged over for his side's first try of the game.
It was not be though, as a magnificent pass from Giteau allowed Wallaby captain George Gregan, winning his 105th cap, to canter in under the posts as Australia wrapped up the win with a clinical breakaway try.
Scotland: H Southwell; C Paterson, B Hinshelwood, A Henderson, S Lamont; D Parks, C Cusiter; A Jacobsen, G Bulloch, 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 (cap); B Young, J Paul, A Baxter, J Harrison, D Vickerman, G Smith, P Waugh, D Lyons.
Replacements: M Dunning, B Cannon, R Samo, S Hoiles, E Flatley, M Rogers, W Sailor.