South Africa set Australia a target of 288 to win the third and final Test at Newlands Cricket Ground in Cape Town, sending the series decider to a fifth and final day.
The series between Australia and South Africa is locked at 1-1 going into the last day, with the winner to move to the top of the ICC Test rankings.
Australia won the first Test of the tour in Durban by 214 runs. South Africa hit back to win the second Test in Gqeberha by an innings and 31 runs.
South Africa made 329 in their first innings at Newlands. Australia replied with 429 to take a first-innings lead heading into the second half of the match.
South Africa's second innings closed on 387, a lead of 287 that left Australia needing 288 runs to win on the final day.
Ryan Rickelton, the South African batter, made 101 off 219 balls in the second innings before he was run out. Josh Inglis made a diving save in the field to complete the dismissal.
Wiaan Mulder, the South African batter, reached his century with three sixes and finished on 115 off 221 balls. It was his third Test century, and his second century at Newlands in as many Tests at the ground.
Rickelton and Mulder put together a partnership of 154 runs for South Africa in the second innings.
South Africa then lost their last four wickets for just 16 runs. Marco Jansen was out for a duck in the collapse.
Mulder added 22 runs with Kagiso Rabada before he was eventually out trying to hit Pat Cummins for six, miscuing a shot to Mitchell Starc at mid-on.
Starc finished with 3-65 in South Africa's second innings. Nathan Lyon had earlier dismissed Temba Bavuma.
Cummins dismissed Matthew Breetzke, the South African batter who made 43 off 121 balls, with a short ball. Gerald Coetzee was run out by a direct hit from Marnus Labuschagne.
Australia are now chasing a target that would be their biggest successful fourth-innings run chase since Pat Cummins made his Test debut at the Wanderers in 2011. It would also be the second-largest successful run chase in the history of Test cricket at Cape Town.
South Africa will resume the final day looking to defend 288, while Australia will need to reach the target to win the Test, decide the series and claim the number one position in the ICC Test rankings.