Australia declared their first innings at 565 for five with a lead of 115 in the hope of grabbing early wickets to force an unlikely victory on a batting-friendly pitch.
South Africa lost Alviro Petersen (5), captain Graeme Smith (23) and Hashim Amla (38), but Jacques Kallis and AB de Villiers denied Australia further inroads.
At the tea interval Kallis was unbeaten on 40 and de Villiers was not out one. The tourists are effectively four wickets down with JP Duminy unable to bat after suffering a series-ending Achilles injury.
Petersen fell before lunch and tempers boiled over as Australia's bowlers sought a big breakthrough in the middle session before Smith went after a fiery over from James Pattinson.
The young firebrand worked over the Proteas skipper before getting a thick edge to Rob Quiney in the gully as he attempted to drive outside off-stump.
Amla survived a second review on 20 after Pattinson appealed for a catch behind and Peter Siddle thought he had his wicket on 28.
But the Australians were unable to seek a review because they had run out of referrals and umpire Asad Rauf had words with a fired-up Siddle after a short sharp exchange with Amla.
Spinner Nathan Lyon proved expensive, going for 26 runs off his two overs before he was removed from the attack.
But Siddle finally got Amla's wicket when he hit firmly to Michael Hussey in the covers for 38, leaving his team 102 for three.
Australian skipper Michael Clarke earlier declared when he was unbeaten on 259 with wicketkeeper Matthew Wade 19 not out.
Clarke eclipsed England's Alastair Cook's 235 not out two years ago as the highest individual score at the Gabba. Don Bradman hit 226 at the ground in 1931.
Australia went after quick runs before the declaration. Hussey had a nervy spell before clinching his 17th Test century and was out for 100 on the next ball he faced from Morne Morkel.