The visitors scored tries through Tatafu Polota-Nau, Adam Coleman, Michael Hooper and Kurtley Beale as they withstood some intense pressure from Wales, whose tries came via Steff Evans and Hallam Amos.
It was a 13th straight win for the Wallabies over the Welsh, who they will meet again in the pool stages of the next global championship in Japan in two years’ time.
Wales coach Warren Gatland, back at the helm of the side after his spell with the British and Irish Lions, had said in the week that he believed his side could win the World Cup, but on this evidence they will need to be more clinical with ball in hand to profit from their possession.
"You have to be more clinical against a side of that quality," Gatland told reporters. "We tried to force a few too many passes and offloads but that’s what we’ve been encouraging the players to do."
Australia showed muscle among the forwards for the opening try as they claimed a lineout 10 yards from the Wales line and drove their way over through hooker Polota-Nau.
The Welsh hit back a few minutes later when scrumhalf Gareth Davies breezed through a rare gaping hole in the Australian defence and as they took the ball through the phases, Leigh Halfpenny fed Evans to score out wide.
The end-to-end battle continued and Australia were finding joy with kicks behind the Welsh defence. When flyhalf Bernard Foley’s clever chip into the corner had the hosts scrambling, Will Genia played lock Coleman into a gap to score from close-range.
Australia grabbed the initiative on the stroke of halftime with a third try as loose-forward Hooper barged his way over the line for a 22-13 lead at the break.
Wales enjoyed a period of possession but were held at bay by some ferocious defending and when Beale ripped the ball from the hands of Evans on the halfway line, the fullback raced clear to score unopposed and the visitors’ lead ballooned to 13 points.
Wales grabbed a late consolation when wing Amos dotted down in the corner, but after Halfpenny missed the difficult conversation their hopes of snatching a dramatic late victory were dashed.
There was some concern for the home side when injured centre Jonathan Davies had to be assisted from the field at the end of the game.
"We just hung in there. Wales played really well and were on the front foot from the first minute. We defended really well under difficult circumstances," Australia coach Michael Cheika told BBC Two.
Australia face England, 21-8 winners against Argentina on Saturday, at Twickneham next weekend, while Wales host Georgia.
(Reporting By Nick Said; Editing by Rex Gowar)
