Wings Bryan Habana and Lwazi Mvovo scored two first-half tries in three minutes for the Springboks, who led 20-9 at the break, while flyhalf Pat Lambie contributed 16 points with his boot.
The Pumas, who notched four tries in Durban as they condemned South Africa to bottom spot in the Rugby Championship, failed to breach the visiting defence as their points came from four penalties by flyhalf Nicolas Sanchez.
The Springboks, who made eight changes to their side, showed the grit and urgency lacking last week and put Argentina under almost constant pressure as they ended a run of three defeats.
Lambie had a fine playmaking game, trying a chip over the defence, a grubber effort and a crossfield kick to set up attacks in the opening half hour and he also booted a drop goal early in the second period.
South Africa had a scare at the start when Juan Imhoff, who scored the first ever hat-trick against the Springboks in Durban, broke through on the wing and only a last-ditch tackle from lock Eben Etzebeth prevented a try.
That determined tackle set the tone for the visitors who went on to starve Argentina of possession and, when the hosts attacked, gave them little chance to get close to their line.
Habana went over in the corner after 27 minutes when he took a pass from scrumhalf Ruan Pienaar who five minutes earlier was denied a try by a last-gasp tackle.
Mvovo then broke inside from his wing, skipped past two tackles and was brought down but stretched out to touch down just over the line.
South Africa coach Heyneke Meyer will have been pleased with his team’s reaction to their first defeat by Argentina in their 20th meeting last weekend as he draws up his World Cup squad.
Daniel Hourcade’s Argentina took a step backwards in terms of their precision and discipline, giving away several penalties for not releasing the ball when down, and he will mull over his options before naming his squad on Sunday.
South Africa open their World Cup campaign with a Pool B match against Japan on Sept. 19 while Argentina face holders New Zealand in Pool C the next day.
(Reporting by Rex Gowar, editing by Tony Jimenez)