Taniela Tupou, Filipo Daugunu and Tom Wright all crossed for tries as an energised Australia kickstarted a new era after the chaotic tenure of Eddie Jones.
A bruising first-half in front of 35,945 fans saw two yellow cards -- one for each side -- and ended with the hosts just three points ahead at 13-10.
The Wallabies turned on the afterburners in the second half, capped by a sensational 60-metre solo try from weaving fullback Wright that broke the Welsh resolve.
"Great result, we've put in a good few weeks of work now. This squad's got really tight," said Wallabies skipper Liam Wright, after his first match at the helm.
"We weren't perfect tonight by any means but I thought there was a lot of grit we showed out there in front of a huge home crowd."
Schmidt was content, but not getting carried away.
"I love the result, but lots to do around the performance," he said.
"The first 20 minutes I felt we did some pretty good things, but then we kind of went off the boil and we really had to work hard from there."
Flashes of brilliance
It was nevertheless an encouraging start for the New Zealander, who took over from Jones after Australia's disastrous 2023 World Cup campaign where they failed to make the quarter-finals for the first time.
Despite limited preparation, his new-look squad, with a host of debutants, showed flashes of brilliance.
They dominated possession, a trait he instilled in Ireland when he led them to become the number one team in the world, and won the breakdown battle.
But they also suffered from ill-discipline, conceding 12 penalties.
Wales's discipline was also poor with defeat heaping more pressure on Gatland, whose team thrashed Australia 40-6 at the World Cup but have now lost eight on the trot.
It is their longest run without a win since 2012 and they remain winless in Australia for 12 matches stretching back to 1969, with one more Test in Melbourne next week to stop the rot.
'Proud of the fight'
"We started well in the first half, but probably a couple of mistakes cost us a few points and discipline let us down," said Wales captain Dewi Lake.
"Always proud of the fight, we don't step on the field to lose games, but we're still chasing that win."
Wales arrived without several injured players, and made six changes from the team that lost heavily to South Africa a fortnight ago.
They opened the scoring when Ben Thomas nailed a long-range penalty in the second minute after a dangerous tackle by James Slipper.
But the hosts hit back immediately with a penalty of their own, converted by Noah Lolesio who slotted another from distance soon after to give them the lead.
With Australia seeing far more of the ball, the first try came on 20 minutes with big prop Tupuo barging over after a series of pick and drives.
Adding to Welsh woes, prop Gareth Thomas was sin-binned.
But the visitors persevered and won a penalty try minutes later after a maul was pulled down, which saw Australia's Fraser McReight yellow-carded to leave the sides with 14 men each.
Wales levelled the scores soon after the interval with a successful penalty, but winger Daugunu then spotted a gap on the right and darted through with his momentum helping him slide over the try line.
Another pin-point penalty from Thomas narrowed the gap to two points with 15 minutes left before Wright's cracking try and Tom Lynagh's conversion put the game beyond reach.
