The Socceroos took an early lead through Brett Holman before Harry Kewell was shown a straight red for a handball on the goal-line and Asamoah Gyan slotted home his second penalty of the tournament.
But Ghana side struggled against Australia's 10 men, showing limited creativity and resorting to shot after shot from long range.
And it was Australia who came closest to winning the match when Luke Wilkshire failed to beat Black Stars goalkeeper Richard Kingston when clean through on goal.
It was a better display from the Australians who had been lambasted by their national press after a meek opening performance in losing 0-4 to Germany.
GROUP D STANDINGS
TEAM W-D-L F:A Pts Ghana 1-1-0 2:1 4 Germany 1-0-1 4:1 3 Serbia 1-0-1 1:1 3 Australia 0-1-1 1:5 1