Australia toiled, taking a single wicket in the opening two sessions before a burst after tea, but it was still very much the home side’s day and sets up an intriguing tussle on Saturday.
Mulder top-scored with 115, his fourth test century, while Rickelton amassed 101 as the pair ensured Australia will need to complete the second highest successful run chase in 137 years of test cricket at Newlands.
The highest was achieved by Steve Waugh's Australia side in 2002 when they chased down 331 to clinch the series.
The pitch is starting to show signs of wear, with Australia batter Josh Inglis saying on Thursday a chase of over 200 would be a difficult one batting last.
They will need considerably more than that at more than three runs an over against a South African bowling attack that has had its feet up for more than a day-and-a-half.
South Africa resumed on the fourth morning at 140 for four and lost only Matthew Breetzke (43) in two sessions as he fell to a pull shot and was caught on the boundary, a familiar mode of dismissal for the home side this test.
Rickelton and Mulder put on 154 for the sixth wicket as they took few risks and accumulated runs.
There was considerable turn for spinner Nathan Lyon (2-101) and variable bounce for the seamers.
Mulder was the last man out as he tried to up the tempo, caught on the boundary to bring a close to the day.
The series is level at 1-1 after Australia won the first test by 214 runs in Durban and South Africa responded with a victory by an innings and 31 runs in Gqeberha.
The winners of the match will occupy the number one spot in the test world rankings, which is currently held by Australia.