South Africa captain Temba Bavuma has praised his team's resilience and character after their remarkable 176-run victory over Australia in the series-deciding third Test at Newlands, a triumph he rated as the best of his career.

Having been effectively 40 for 4 in their second innings at the start of day four, South Africa looked down and out before centuries to Ryan Rickelton and Wiaan Mulder engineered a fightback as they set Australia a fourth-innings chase of 288 runs.

The match appeared evenly poised heading into the final day of an absorbing series. But quick Kagiso Rabada knocked over Australia's top three with the new ball before offspinner Simon Harmer claimed career-best figures of 6 for 16 off 21.4 overs as the tourists were routed for 111.

"There were honest conversations that we had yesterday," Bavuma said at the post-match presentation. "I think a lot of them were about the character of the team and that coming out.

"So when the batters were able to do what they did, Ryan Rickelton and Wiaan Mulder, putting us in a competitive position like that....the bowlers had the confidence.

"I think the way Rabada started today, he kind of got everything going, and from there we just managed to keep a tight grip on things."

South Africa's series victory was achieved the hard way after their 214-run defeat in the opener in Durban. It was a particularly rusty return to Test cricket, with South Africa having not played the format for almost a year. But they found their groove and dug deep to eventually overwhelm and outplay Australia in a rock fight of a series.

"We at times found ourselves in awe of the Australians," Bavma said. "I think a lot of it for us was, I guess, that whole South African trait of resilience.

"We seem to play a lot better when we're behind the game, whether that's a good or a bad thing...you know that's for us. I think the fans and everyone globally have been treated to proper cricket."

Having beaten Australia last year at Lord's to win the World Test Championship, this series victory against their old foe adds to the growing list of achievements under Bavuma's captaincy reign.

The win also leapfrogged South Africa over Australia to the top of the ICC Test rankings.

"That [No.1 ranking] is exceptional. I think that's obviously been a part of our ambition as a team," Bavuma said. "We're trying to push that standard as high as we can.

"With this opportunity that we have, we want to leave the Proteas badge in a better place. So we'll definitely celebrate that milestone as a team.

"Every time you get an opportunity to come up against Australia, you savour that. I don't think I've been involved in a better series. So yeah, this is definitely there at No.1 [best Test win]."