But the Wallabies will return home with five points from their two matches after their bonus point win in Johannesburg. They came close to a losing bonus point, but James O’Connor missed two penalty attempts in the dying minutes.
The Springboks had to be satisfied with four points for the win – and will have to travel to New Zealand knowing they will need at least one win in two matches against the All Blacks if they are to have a chance of defending their Championship title.
The Springboks went ahead through two penalty goals by Pollard in the first five minutes, while the Wallabies suffered a blow when fullback Tom Wright left the field with an injured left knee.
Wright, one of the stars of Australia’s win in Johannesburg, turned awkwardly on a field which was soft and yielding after rain during the week and earlier on Saturday.
But the Wallabies struck back almost immediately with a smart piece of opportunism by veteran scrumhalf Nic White, who kicked into empty space after Australia were awarded a free kick from a scrum.
Left wing Corey Toole, playing in his first Test, gathered the ball and scored a try without being touched.
When White was caught in possession near his own line minutes later, Pollard took advantage of the turnover with a cross kick which enabled right wing Canan Moodie to score.
It was a double blow for the Wallabies because White suffered a head injury in the collision and was replaced by Tate McDermott with the Springboks leading 13-7 after a frenetic opening 11 minutes.
Wallaby captain Fraser McReight crossed the Springbok line three minutes later but the try was ruled out because of a knock-on.
Eighthman Kwagga Smith, a late replacement for Jean-Luc du Preez, scored South Africa’s second try five minutes before half-time after a drive from a lineout.
As they did in Johannesburg, where they overcame a 22-point deficit, the Wallabies came back strongly in the second half with a try by right wing Max Jorgensen.
Pollard put South Africa 23-17 ahead before replacement hooker Brandon Paenga-Amosa scored a try for the Wallabies 11 minutes from time.
O’Connor, however, missed a conversion attempt from the touchline that would have given the tourists the lead.
Replacement lock Eben Etzebeth sealed South Africa’s win with a converted try six minutes from time.