The result maintained the perfect record of the Springboks against the Wallabies at Loftus Versfeld as they notched up an eighth straight victory having led 17-5 at half-time.
Australia opened and closed the scoring with tries from Marika Koroibete and Carter Gordon, but South Africa recovered quickly in the first half and dominated the second.
Ill discipline cost the Wallabies dearly after half-time as David Porecki and Suliasi Vunivalu were sent to the sin bin having conceded penalty tries.
It was a nightmare start for Eddie Jones in his second spell as coach of Australia, who lost nine of 13 internationals last year.
He labelled the South Africa side "half baked" before the match because they sent many of their stars to New Zealand ahead of the game to acclimatise for a July 15 clash with the All Blacks.
But it was opposite number Jacques Nienaber who had the last laugh having predicted during the week that his weakened side would be good enough to start the season with a victory.
However, neither Nienaber, those in the 50,089 crowd, nor thousands watching on TV would have imagined victory could be achieved by such a wide margin.
Australia were first to score on a chilly winter evening as a passing movement set up Koroibete to brush off Andre Esterhuizen and score in the corner. Reece Hodge failed to convert.
Hodge fluffs kicks
Manie Libbok, whose kick dropped just short with an ambitious penalty attempt from his half, succeeded with his second effort closer to the posts and South Africa were on the scoreboard.
Arendse scored his first try on 16 minutes to put the Springboks ahead as pressure pushed the Wallabies back and when the ball went wide, the winger had the simple task of dotting down.
Libbok converted and, within eight minutes, the reigning world champions had turned a five-point deficit into a five-point advantage.
Hodge was wide with a long-range penalty shot before Arendse struck again at the ground where he plays his club rugby for the Bulls.
He darted down the blindside to score and a high conversion kick from Libbok sailed between the post for a 17-5 lead they retained until half-time.
Australia had a chance to reduce arrears after the hooter sounded to signal the end of the first half, but Hodge failed again, with his 66-metre shot falling short.
Instead of an Australian recovery in the second half, South Africa took control and Arendse completed his hat-trick on 51 minutes by wriggling past three defenders to score.
Then came two penalty tries which left South Africa 36-5 ahead with a quarter of the match still to be played.
Pieter-Steph du Toit barged over for another Springbok try, converted by Libbok, before substitute Gordon scored a late consolation try which he converted.
The first round continues later Saturday when Argentina host defending champions New Zealand in Mendoza.
