Wales floored a Tri-Nations heavyweight for the first time since 2005 as they ended their autumn test series on a high.
The reigning RBS Six Nations champions produced some scintillating rugby in patches as wing Shane Williams and full-back Lee Byrne scored memorable first-half tries.
Williams, recently-crowned International Rugby Board player of the year, rounded off a breathtaking fourth-minute move, then transfixed Australia's defence by sending Byrne over.
Australia, who were really outclassed when Wales attacked, saw their hopes of a first unbeaten European test match tour since 1996 evaporate. But their doggedness meant Wales could never relax, and they were ultimately indebted to out-half Stephen Jones booting two penalties, a drop-goal and conversion.
Lock Mark Chisholm and wing Digby Ioane scored tries for Australia at either end of the contest, while Matt Giteau kicked eight points.
Jones' drop-goal on 67 minutes seemed to calm Welsh nerves and with the forwards scrapping ferociously for possession, Australia could not get up a head of steam.
Jones then booted a long-range penalty with two minutes remaining, and although Ioane collected a last-minute try, Wales were home and dry, if somewhat breathlessly.
But they will now launch their Six Nations title defence buoyed by a victory they richly deserved.
Wales L Byrne; M Jones, T Shanklin, J Roberts, S Williams; S Jones, G Cooper; G Jenkins, M Rees, A Jones; I Gough, A-W Jones; R Jones, M Williams, A Powell Subs A Bishop for Roberts, 17 mins; D Jones for Powell, 61 mins
Australia D Mitchell; P Hynes, R Cross, S Mortlock , D Ioane; M Giteau, L Burgess; B Robinson, S Moore, A Baxter; M Chisholm, N Sharpe; H McMeniman, P Waugh, R Brown Subs Q Cooper for Mortlock, 2 mins; L Tuqiri for Hynes, 33 mins; G Smith for Waugh, 62 mins; D Mumm for McMeniman, A Freier for Moore, both 69 mins
Referee Alan Lewis (Ireland)