Not since November 2008 had Wales beaten the Wallabies, who had racked up 13 straight consecutive wins over Warren Gatland's side.
Two penalties from Leigh Halfpenny and a nerveless late three-pointer from Dan Biggar was enough to make it seven straight wins for Wales in a match riddled with handling errors.
It could have been even more comfortable had the usually reliable Halfpenny not missed two simple kicks by his lofty standards in an arm-wrestle of a contest.
Australia, though, has now won just three of 11 Tests in 2018 and the pressure will only continue to grow on under-fire coach Michael Cheika just a year out from the Rugby World Cup.
There was little of note in an attritional first half, with Halfpenny's wayward kicking the main talking point.
The full-back had already missed a relatively simple effort by the time he split the posts to put Wales on the board.
Australia was looking the more likely to score a try, but only had a Bernard Foley three-pointer to show for its efforts after Wales was pinged for offside.
The home side should have gone in front before the break, a shocked Halfpenny pushing a simple effort in front of the posts wide.
The game became increasingly scrappy in the second half, with Australia guilty of knock-ons at key moments and Wales equally frustrating with a couple of nudges forward.
Halfpenny had the chance to exorcise his first-half demons with 12 minutes remaining, though, after Australia was pulled up for an infringement at the ruck.
From a similar position to his first half shocker, Halfpenny again did not make the cleanest contact but did manage to just land the effort inside the right-hand post.
The home crowd let its annoyance known when Halfpenny was wiped out by Samu Kerevi. There was seemingly no malice but did appear to be shoulder-to-head contact.
Shortly after the frustrations were worsened when Wales was pulled up for holding and Matt Toomua nailed a lengthy kick from the right touchline.
Biggar, on as a replacement for Halfpenny, kept his cool with a kick from the 22 line when Australia was guilty of laying in on the ruck and Wales celebrated a famous win.