The Australians are going for their third gold in a row but suffered a surprise 2-1 defeat by Germany in the first round.
"Those were three points we desperately needed but we can still, without a doubt, improve our performance. The first half was a very ugly game," coach David Bell said.
Earlier, world champions Argentina took a while to wake up after an 8:30 a.m. start but eventually pushed through Japan's neat defence 3-1 for their second victory, staking their claim to a first Olympic gold.
Australia got off to a messy start, mispassing and regularly allowing South Africa into the circle. It was only thanks to the quick reactions of goalkeeper Rachel Imison that South African striker Pietie Coetzee did not find the back of the net.
Ball control was made much harder by a squally seaside wind whipping around the stadium but towards the end of the first half, Australia settled down and set up a field goal from Julie Towers and a penalty from Suzie Faulkner.
Their third came from Peta Gallagher, who tapped in a cross.
Argentina, known as Las Leonas (The Lionesses), were under pressure for the first 20 minutes against Japan until they smacked the ball diagonally across from deep left field, through a stunning midfield run by Luciana Aymar to scorer Ines Arrondo.
Rika Komazawa scored Japan's first Olympic goal to level but Argentina kicked into gear, wore down the midfield and set up two more goals.
"We struggled to begin with but we're Argentine -- we find it hard to get up that early," Marina di Giacomo said.
