Captain Temba Bavuma led from the front with a superb 179, earning the Player of the Match award as South Africa recovered from their first-Test defeat to deliver an emphatic response.
Australia showed some resistance on the final day, but South Africa's bowlers eventually broke through to complete the victory and leave the visitors with too much to do.
Bavuma was delighted with his contribution, particularly given the difficult batting conditions throughout the match.
"Definitely, there at the top is one of my best," he said of his innings. "We saw throughout the days that batting was quite difficult, especially against the new ball."
The South African captain said he took great pride in helping his team establish a strong position and giving them a chance to level the series.
"I take a lot of pride in that, but also to make a play in us having a chance within the series," Bavuma added, explaining that he would take plenty of confidence from the performance.
He also praised the contributions of his team-mates, highlighting Kagiso Rabada's importance to the bowling attack and Marco Jansen's impact with both bat and ball.
Bavuma believes South Africa's ability to remain patient and wear down their opponents was central to the victory.
"When we were batting, for me, it was all about how we can extend it, how we can go another hour, another hour becomes a session," he explained.
He added that the team had been urged to become more ruthless when opportunities arose, and he was pleased with the way they applied that approach in Australia's second innings.
"We play good old Test cricket, try and wear the opposition down and then take them down when the opportunity presents itself," Bavuma said.
Australia captain Pat Cummins acknowledged that his team had fallen well short of their best, despite some resistance on the final day.
"There was some good fight today. Boland and Trav played their roles. But it was a fair way to come back from there and it wasn't enough," Cummins said.
The Australian skipper admitted that his side had struggled across several departments and needed to improve ahead of the deciding Test.
"We were a long way away from our best. We didn't start off too strong. Today, across the board, we didn't contribute," he said.
Cummins insisted that the balance of the team was not the main concern, instead pointing to the need for greater contributions from the batting and bowling units.
He also acknowledged that Australia had failed to make enough runs on a pitch that offered opportunities, while praising the determination shown by Scott Boland and Travis Head.
The result sets up a decisive third Test in Cape Town, with both teams level at one win apiece. South Africa will take confidence from their commanding performance, while Australia must regroup quickly to regain control of the series.
South Africa produced a commanding performance to defeat Australia by an innings and 31 runs in the second Test at St George's Park in Gqeberha, with captain Temba Bavuma leading the way with a magnificent 179.
Marco Jansen took a five-wicket haul as the Proteas skittled Australia out for just 99, before the tourists found themselves in trouble following-on at 156-4, still trailing by 170 runs.
Springbok legend Victor Matfield believes the world champions will play with more of an attacking edge on their tour of Europe after leaning heavily on their traditional physical strengths during Rugby's Greatest Rivalry series.
Proteas captain Temba Bavuma struck his fifth Test century, and the best of his career, as the hosts dominated Australia on the third day of the second Test at St George's Park in Gqeberha.
