The Wallabies, though, hit back quickly, and thought they had grabbed their first try when loose forward Lukhan Salakaia-Loto galloped over, but referee Paul Williams called them back for a forward pass by Samu Kerevi.
Esterhuizen was somewhat unlucky to be yellow-carded for a dangerous tackle on Wallaby fullback Tom Banks, who had been close to the ground when the Bok No 12 tackled him around the neck area.
But the Boks weren’t affected by playing with one man less. In fact, they scored again in the 24th minute when Pieter-Steph du Toit surged through a gap and then chipped ahead.
Herschel Jantjies chased the ball down, and even as he was stopped just short, Lood de Jager forced his way over.
At 14-3 up, the Boks were flying, with the key to that being the snappy service and tempo provided by the scrumhalf Jantjies, and greater belief among the South African backs the longer the game went on.
But Australian rugby players are renowned for their creativity on attack, and they looked dangerous whenever they gained possession upfront.
They struck back near the half-hour mark when wing Dane Haylett-Petty finished off smartly in the right corner to reduce the deficit to 14-10.
And just four minutes later, they may have felt that they would take the lead when Haylett-Petty went down to pick up the ball just short of the line, but he spilled it forward to let the Boks off the hook.
Rassie Erasmus’ team couldn’t continue the momentum from the first half after the break, but they got an edge when Aussie tighthead Taniela Tupou was yellow-carded for a shoulder charge into a ruck.
And the Boks pounced almost immediately, with some wonderful handling – especially from captain Eben Etzebeth – resulting in Sbu Nkosi finishing before the hour mark.
Herschel Jantjies crowned a memorable debut with a typical scrumhalf try when he broke down the short side to stretch the lead to 28-10 and virtually wrap up the win with 20 minutes to go.
What a win - well done boys, a full-house of five log points, and five tries to boot! 💥💥💥💥💥
The Wallabies brought on Kurtley Beale to add some firepower to their attack, and the Waratahs star pulled off a superb offload for Bernard Foley to run it in under the posts.
The Boks were chasing a bonus point in the last few minutes, and Reinach got the breakthrough to complete a satisfying outing for the ‘B team’ ahead of next week’s showdown with the All Blacks in Wellington.
Springboks 35 – Tries: Herschel Jantjies (2), Lood de Jager, Sbu Nkosi, Cobus Reinach. Conversions: Elton Jantjies (5).
Wallabies 17 – Tries: Dane Haylett-Petty, Bernard Foley. Conversions: Foley (2). Penalty: Foley (1).