The Six Nations champions took charge of Pool D with a second successive win that could lead to a last-eight clash against France or Argentina.
Here, the PA news agency wraps up all of the thrilling action from day 10 in Japan and takes a look ahead to Monday's game between Scotland and Samoa.
Wales looked home and dry when they led 26-8 through tries by centre Hadleigh Parkes and scrum-half Gareth Davies.
But Australia reduced their deficit to a single point with the aid of tries from full-back Dane Haylett-Petty and captain Michael Hooper.
However, Wales edged further ahead through Rhys Patchell's 72nd-minute penalty and held on to beat the Wallabies for just the second time in the last 15 Tests following a scintillating contest.
Georgia bounced back from their opening World Cup defeat to Wales with a comfortable 33-7 bonus-point Pool D victory over Uruguay.
Georgia's superior strength was too much for Uruguay to handle as the Lelos ran in five tries at Kumagaya Rugby Stadium, with Uruguay replacement Facundo Gattas sent off late on for another poor high tackle.
Uruguay were reduced to 14 men three minutes from the end when Gattas left English referee Wayne Barnes with little option after a no-arms tackle, with his shoulder making contact with the head of Georgia flanker Shalva Sutiashvili.
Wales were already 16-8 ahead when scrum-half Gareth Davies intercepted a pass on halfway and sprinted clear to score his side's second try of the game.
Rhys Patchell's conversion put Wales 15 points in front, ending an opening 40
minutes they had dominated.
Gregor Townsend insists Scotland are not under extra pressure – despite admitting they face World Cup elimination if they fail to beat Samoa on Monday.
The Dark Blues have no room for error after being thrashed by Ireland in last Sunday's Pool A opener.
Japan's shock win over Joe Schmidt's men means bonus points could now have an impact but the Scots must overcome the Pacific Islanders, Russia and then hosts Japan if they want to keep their hopes of progressing to the last eight alive.
"The reality is we now have to win our next three games to make it out of our pool, so the knockout stages for us begin this Monday night," Townsend said. "I firmly believe this group are ready to take on that challenge."