Jacques Nienaber made 10 alterations to his starting line-up after a series-clinching win over British and Irish Lions last weekend, but the Springboks were too strong for the Pumas.
Cobus Reinach raced away for a sublime breakaway try and Aphelele Fassi finished clinically in the first half for the world champion at Nelson Mandela Bay Stadium on Sunday (AEST).
Elton Jantjies scored 17 points with the boot to keep South Africa in command and Hendrikse came off the bench to go over in the closing stages.
Argentina could only muster four Nicolas Sanchez penalties as the Springboks made it 10 wins in their past 11 Tests in their first Rugby Championship match since winning the 2019 tournament.
Reinach capitalised on a loose pass to dart away from inside his own half and score a superb try that was brilliantly converted by Jantjies, who had opened the scoring with a penalty.
Sanchez got the Pumas on the board from the tee, but wing Fassi showed great hands to keep a clever kick from Jantjies in and crossed in the left corner after a juggling act.
South Africa was bossing the forward battle and went in at the break with a 21-9 lead after two penalties apiece from the livewire Jantjies and Sanchez.
The trusty boot of Sanchez reduced the deficit to nine points early in the second half, but Jantjies responded by sending another two kicks sailing between the posts.
Backs saw little of the ball in a bruising battle and Fassi had what he thought was his second try of the match ruled out, as Malcolm Marx played the ball on the ground in an earlier passage of play.
Hendrikse put the icing on the cake when he went over in the corner after a powerful run from Marco van Staden.