Wales rediscovered their Grand Slam swagger to claim their first win over Australia since 1987 in a pulsating encounter at the Millennium Stadium.
Clinical Wallaby finishing gave them the early lead with tries from the superb Lote Tuqiri and Nathan Sharpe.
Wales' scrum power won a penalty try, before a spectacular Shane Williams score took the home side clear.
Tuqiri set up a fantastic Chris Latham try, but Mat Rogers missed the conversion and the home side clung on.
Gareth Thomas and Matthew Watkins sparked thrilling early attacks as the home forwards took a grip, especially at the scrum.
Stephen Jones landed a penalty before Williams - under pressure on his own 22 - stepped Drew Mitchell to spark a length-of-the-field attack.
But dogged Wallaby defence and Welsh errors denied the home side another score, and when Australia won clean line-out ball on the half-way line they showed the meaning of clinical finishing.
Rogers looped around in midfield and broke the defensive line, before finding the supporting Tuqiri who crossed under the posts.
Phil Waugh went close to a second try, only to be denied by an excellent Dafydd James cover tackle.
Another James hit on Mitchell nearly set up a Martyn Williams try, but the home side - with Colin Charvis leading the forward effort - had to be content with a second Jones penalty before half time.
The second period opened disastrously for Wales, Thomas putting Shane Williams under pressure in defence and giving Australia turnover ball.
Latham nearly got through, but Sharpe quickly picked up to burst under the posts for the second try.
Wales turned the screw up front with a series of powerful scrums, but James failed to put Williams over from a clear overlap.
The forwards kept up the pressure, and after the Wallabies collapsed three scrums in the shadow of their posts referee Tony Spreadbury awarded Wales a penalty try.
Australia fired back, but lost the ball in Wales' 22, sparking the move that nearly blew the roof off the Millennium Stadium.
Tuqiri was the major threat to Wales
Gareth Cooper moved the ball left, Thomas feeding Shane Williams whose grubber kick bounced into Thomas' hands.
He passed back to Williams, who had the pace to out-sprint Tuqiri for the try.
Australia hauled off captain George Gregan, as Jones extended Wales' lead with three penalties to Rogers' one.
But Tuqiri was ever-threatening, and in the 72nd minute he broke a Stephen Jones tackle from deep in his own half.
He powered through before a beautiful grubber kick found Latham, the full-back controlling well for a fine try.
Rogers missed the conversion to leave Wales a slim two-point lead that they were able to hold in a tense finale.
Wales' 1987 win was against a 14-man Australia at the inaugural World Cup in Rotorua, the last victory in Cardiff coming in 1981.
It was also the first win over any of the three southern hemisphere superpowers since the 29-19 triumph over South Africa in 1999.
Wales: G. Thomas, James, Watkins, Parker, S. Williams, S. Jones, Cooper, D. Jones, R. Thomas, Horsman, Gough, Sidoli, Charvis, M. Williams, Owen.
Replacements: Sweeney for S. Jones (80), Davies for R. Thomas (34), A. Jones for Horsman (49). Not Used: Evans, J. Thomas, Phillips, Byrne.
Australia: Latham, Gerrard, Tuqiri, Turinui, Mitchell, Rogers, Gregan, Dunning, Cannon, Fitter, McMeniman, Sharpe, Roe, Waugh, Smith.
Replacements: Sailor for Gerrard (64), Whitaker for Gregan (56), Baxter for Fitter (51), Chisholm for McMeniman (70). Not Used: Polota-Nau, Fava, Johansson.
Referee: Tony Spreadbury (England)