“That was an awesome 80-minute performance,” said man of the match Wright.
“Ebbs and flows, we gave a lot of momentum to Wales at stages, we made it difficult for ourselves, but those are games you like to be a part of.”
Wales prop Gareth Thomas admitted his team failed to live up to their planning.
“When we were training in the week we looked sharp, there was a real confidence in the group. Soon as there was a bit of pressure on us we weren’t good enough,” he told Welsh broadcaster S4C.
Tom Rogers was on hand to deprive Samu Kerevi of a try in his 50th Test after Wright and Max Jorgenson combined with smart offloads that cut the Welsh defence to ribbons.
Wright then showed a clean pair of heels down the right wing, stepping inside Blair Murray with ease for the opening try of the game.
Gatland could be seen grimacing at the defensive lapse and things quickly worsened. Nick Frost crossed for Australia’s second just minutes later, the lock galloping in from 50 metres.
Noah Lolesio converted but spurned a penalty shot after Wales full-back Cam Winnett was caught in possession after the restart to go for the corner.
A second penalty saw Australian persistence rewarded as Faessler was driven over from a rolling maul off an attacking line-out with the visitors in total ascendancy, 19-0 up after 22 minutes.
Wright knocked on from the kick-off, handing Wales a rare visit into the Wallaby half, to the delight of the 56,188 crowd at Cardiff’s Principality Stadium, well down on the 74,000 capacity.
The home side made it pay, No 8 Aaron Wainwright crashing over on a short ball for a try converted by Gareth Anscombe.
Then followed a passage of play controlled by Wales, their domination resulting in two Anscombe penalties that suddenly saw the Welsh back within six points going into halftime.
Australia enjoyed the worst possible start to the second period when Kerevi was yellow carded by New Zealand referee James Doleman for a high, head-on-head tackle on Jac Morgan.
That card was upgraded to red as there were no mitigating factors, although Kerevi was replaced after 20 minutes under new laws World Rugby are trialling.
The question then was whether Wales could capitalise on their numerical advantage, something they failed to do in their 24-19 loss to Fiji last week.
They failed again, Lolesio again going to the corner with an offside penalty, Faessler driven over from the resulting maul for his second try of the game.
There was deja vu just minutes later after Wales skipper Dewi Lake was penalised: Lolesio kicked to the corner and Faessler was on hand to peel off a maul and plough through Ben Thomas' tackle for his hat-trick of tries.
Lolesio made no mistake with the extras and suddenly Australia were 33-13 up despite Kerevi warming the bench.
Wales looked increasingly toothless in attack, a raft of replacements disrupting any continuity they might have had, notably at the line-out where replacement Ryan Elias failed to find his mark on a number of occasions.
And Wright grabbed an interception try off a Sam Costelow pass for an easy run-in.
Rugby league convert Joseph-Aukuso Suaalii made his entry on 62 minutes as Kerevi’s replacement, Australia having notched up three converted tries while down to 14 men.
Wales hit back with a Ben Thomas try, Costelow converting, but the Wallabies had the final word as first Len Ikitau outstepped Winnett and player-of-the-match Wright scored his third and Australia’s eighth of a one-sided match.
