Their form in the lead up has been good, and their first ever win will boost confidence.
"I was just delighted with the result and the performance," Australia's Scottish-born coach Tom Sermanni said. "It certainly eased the pressure on the team and the coach.
"I think it will boost our confidence and it was a combination of the win and the performance because Ghana are a good side and they had a lot of possession.
"We defended well and I think we created a lot of chances. So I think we came away with a lot of positives tonight," Sermanni said.
Norway, ranked fourth in the world, and Canada, ranked ninth, are also in Group C and are favorites to pass into the knockout round ahead of Australia, who are 15th in the FIFA rankings.
The lowest ranked team in the current tournament at 47, Ghana have appeared in two previous World Cups without getting beyond the group stage.
Sermanni said that the next hurdle against Norway on Saturday would be a difficult one for the Australians, but he predicted that the crucial tie would come against Canada in the final group game on Sept. 19.
In other Women's World Cup group stage games yesterday, it was:
Group C
Norway 2, Canada 1
Group D:
China 3, Denmark 2
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