A last-minute try for Australia has seen Wales record their fourth loss of the Autumn Internationals series.
Toby Faletau had a chance for a try after 25 minutes, but replays showed that the Wallabies' defence had done just enough.
Australia took a 9-6 lead at half time, each side scoring through penalty kicks.
Leigh Halfpenny did get a chance to level the score just before the break, but his kick sailed wide.
Halfpenny brought Wales level in the 56th minute, and put them ahead four minutes later.
Wales's defence dug deep to hold on to their slender lead until the 79th minute, when Kurtley Beale scored the game's first try.
To add to Wales's woes, Halfpenny was injured in the run-up to the try, needing to be stretchered off the pitch.
Defeat means that Wales will slip out of the world's top eight, and will face two top-ranked sides in their group at the 2015 World Cup.
