South Africa set Australia 288 to win the deciding third Test at Newlands, Cape Town.
South Africa resumed at 140 for 4 with a lead of only 40 runs. Australia were on top.
The pair batted nearly 54 overs together and added 154 runs for the sixth wicket.
The wicketkeeper reached his third Test hundred off 219 balls with 12 fours.
The allrounder reached his fourth Test hundred off 204 balls, hitting 10 fours and four sixes.
Rickelton was run out for 101. Four wickets fell for 16 runs. South Africa were 387 all out.
Starc took 3 for 65 and a match haul of nine wickets. Cummins took 2 for 71.
This would be the second-highest successful chase in 137 years of Tests at Newlands.
The worn surface helps spinner Simon Harmer. Australia must score at over three an over.
Australia were 41 for 4 early on the final day. The chase was falling apart fast.
Rabada removed Travis Head for 14 to claim his 350th Test wicket.
Harmer took two wickets in one over, including Cooper Connolly for a duck.
The series is 1-1. The winner takes the world No. 1 Test ranking from Australia.
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