South Africa's need to rotate players for its fourth test in as many weeks gave an opportunity to Fassi, who scored off a cross-kick from Jantjies to give the home team their second try at Nelson Mandela Bay Stadium.
Fassi hauled the low kick in with his left hand as it drifted toward the touchline, juggled briefly, and regathered to speed clear and put South Africa 15-3 up after 20 minutes.
The Boks were accurate enough to lead 21-9 at halftime despite conceding the territory and possession stats to the Pumas.
Jantjies kicked two more penalties in the second half before Hendrikse celebrated his debut with a try with two minutes to go. He squeezed the ball down with a full-length dive to the corner to give the Springboks a bonus point.
That meant a successful outing for South Africa, who dug deep into their reserve players ahead of a second test against the Argentinians and a fifth test in five weeks next weekend.
The All Blacks still lead the early Rugby Championship standings after their 57-22 victory over the Wallabies.
South Africa won the southern hemisphere's top rugby tournament in 2019 on the way to a World Cup triumph, but withdrew last season and didn't defend their title because of the coronavirus pandemic.
- AP