Fly-half Gareth Anscombe, an early replacement for the injured Dan Biggar, scored 23 points with the boot in Lyon as scrum-half Gareth Davies, centre Nick Tompkins and captain Jac Morgan added the tries to keep Wales top of Pool C.
Defeat heaped pressure on Wallaby head coach Eddie Jones after his side lost for the seventh time in eight Tests since he took over the reins for the second time in January.
Australia's only victory since then was over Tier II Georgia.
But the rot had long set in before that, with Australia now having lost 19 of their last 25 international Tests - including a first-ever defeat to Italy.
They came into this match knowing it was win-or-bust following last week's shock 22-15 defeat to Fiji - the first time they had lost to the Pacific Islanders in 69 years.
And now they have suffered a new record defeat to Wales, who topped their 28-3 win in Cardiff in 1975.
Jones had shuffled his pack, leaving out talented but green fly-half Carter Gordon after his kicking troubles in victory over Georgia and vulnerability in contact against Fiji's destructive tacklers.
But Ben Donaldson proved no upgrade against a pumped-up Wales, who rolled back the years in their best performance since Warren Gatland returned to the helm in December.
Biggar blow
Wales got off to a dream start with a line-out move straight off the training ground as Morgan hit a beautiful line onto Tompkins's inside pass to break through the defensive line and tee up Davies to score by the posts.
Australia almost hit back immediately but some ferocious defence -- a feature of Wales's performance -- held them out as Liam Williams and Louis Rees-Zammit combined to take down marauding prop Angus Bell.
The Wallabies eventually had to settle for a penalty, stroked over by Donaldson.
Wales suffered a massive blow 12 minutes in as Biggar, who had earlier knocked over the conversion, had to leave the field with a shoulder problem suffered tackling Richie Arnold.
Anscombe, though, proved a more than able replacement, despite missing his first kick at the sticks.
A second Donaldson penalty cut Australia's deficit to one point, but they would not trouble the scoreboard again.
Australia dragged down a rumbling maul and the New Zealand-born Anscombe got off the mark with his first three-pointer.
The Wallabies should have hit straight back but Donaldson opted to kick a penalty to the corner rather than take an easy three points and hooker David Porecki overthrew the line-out, allowing Wales to break clear.
Anscombe added two more penalties before the break.
Jones threw on giant prop Pone Fa'amausili at half-time in place of veteran James Slipper, but the Wallabies gave away a penalty in their first scrum of the half and Anscombe duly eked out the lead further.
Morgan icing on cake
Wales were now well on top as their pack crushed the Wallabies again before a delightful chip from Anscombe saw Tompkins win the chase to touch down under the posts.
Anscombe converted and a high tackle from Samu Kerevi allowed him to kick another three points and stretch Wales's lead to 29-6.
Jones had seen enough and hauled off Donaldson on 53 minutes, throwing Gordon into the fire.
It did not help as late on Gordon tried to kick a penalty to the corner but overcooked it and sent the ball dead.
Australia could not stem the tide and their penalty count kept ticking upwards, with Anscombe doing likewise on the scoreboard.
He rounded off a brilliant personal display with a drop goal while Morgan had the last say with a try off a driving maul.
