
Wales built up a 23-8 halftime lead after tries from Hadleigh Parkes and Gareth Davies and added 14 points from the boot of replacement flyhalf Rhys Patchell to hold on and put the Six Nations champions in control of the pool.
The result means Australia, who came back to within a point at one stage following tries from Adam Ashley-Cooper, Dane Haylett-Petty and captain Michael Hooper, now face a potentially tricker tie in the quarter-finals.
After Australia had surged back into the match, it was down to Patchell, on for the injured Dan Biggar, to hold his cool and slot the decisive penalty with eight minutes to go and secure the win.