The Socceroos, who had been thrashed 4-0 by Germany in their opening game, were under immense pressure the moment Harry Kewell was sent off with just 24 minutes on the clock.
The former Leeds and Liverpool winger, in for the suspended Tim Cahill, blocked Jonathan Mensah's goal-bound shot on the line with his right arm.
Kewell complained bitterly at being dismissed by Italian referee Roberto Rosetti, who had already pointed to the spot, arguing that there had been no intent.
But his words, which continued as he was led away down the tunnel, fell on deaf ears and Asamoah Gyan made no mistake with the penalty, just as he had done to condemn Serbia to a 1-0 defeat in the Black Stars' previous game.
This penalty was only enough to put his side level, however, as Brett Holman had capitalised on a strong start from the Socceroos.
Goalkeeper Richard Kingson, the Ghana captain, was at fault as he spilled Mark Bresciano's free-kick into Holman's path in the 11th minute.
Once Kewell was dismissed it was expected that Ghana would go on to inflict further torment on Pim Verbeek's side.
Kevin-Prince Boateng forced Fulham goalkeeper Mark Schwarzer into a fine save just before the break, but Ghana were then guilty of too many speculative efforts from distance.
The 10 men refused to buckle and created chances of their own, with Wigan Athletic goalkeeper Kingson making up for his earlier error by pulling off a fine double stop, first to deny Luke Wilkshire and then substitute Josh Kennedy on the follow up.
Jonathan Mensah, who had replaced his injured namesake John Mensah, in the heart of the defence, almost won it for Ghana when he rose to head just over and substitute Quincy Owusu-Abeyie forced a good save from Schwarzer with a well-struck shot but Australia deserved at least a point.
The Socceroos must now beat Serbia to have a chance of qualifying for the knockout stages while Ghana will go head to head with Germany for the right to finish as Group D winners.
Ghana (4-5-1): Kingson; Pantsil, Jonathan Mensah, Addy, Sarpei; Tagoe (Owusu-Abeyie 56), K-P Boateng (Amoah 86), A Ayew, Annan, Asamoah (Muntari 77); Gyan
Subs (not used): Agyei, Ahorlu, John Mensah, Inkoom, Vorsah, D Boateng, Appiah, R Ayew, Adiya.
Australia (4-5-1): Schwarzer, Wilkshire (Rukavytsya, 85), Neill, Moore, Carney; Emerton, Culina, Holman (Kennedy 68), Valeri, Bresciano (Chipperfield 66,); Kewell.
Subs (not used): Federici, Galekovic, Beauchamp, Milligan, Jedinak, Garcia, Vidosic.