That gave the unbeaten Springboks a bonus point and a total of 12 points from their three matches, four more than second-placed Australia.
Consistency remains key for improving South Africa as they revel in a first Rugby Championship title in a decade, a significant psychological boost a little over a month out from the World Cup in Japan.
Flyhalf Pollard scored two of his side's five tries and kicked five penalties and three conversions for a personal haul of 31 points, his best tally in an global.
This year's tournament was abridged to three matches per team because of the World Cup in Japan starting on September 20.
"It's a fantastic feeling", said Duane Vermeulen, who captained the two-time world champions.
"It's also a good thing for us going into the World Cup".
"We played the best teams in the southern hemisphere so it is good to have this one step up, although a lot of work still needs to be done before the World Cup".
Argentina, which won the previous meeting between the teams, shocked South Africa with a try by winger Santiago Cordero after two minutes.
"But, yes, we are happy with where we are at the moment".
They were made to pay in the 64th minute when Makazole Mapimpi crossed over in the corner to kill the contest.
It was a particularly pleasing score for the Springboks, who have struggled this season to turn mauls into tries.
Pollard and Puma flyhalf Nicolas Sanchez then got locked into a kicking duel, exchanging penalties, before the 25-year-old South African dived over the tryline just before the break to make it 24-13.
The opening half then became a goal-kicking battle between playmakers Pollard and Sanchez with the South Africa kicking three penalties and converting his try in the final minute of the half.
The Pumas conceded a number of scrum penalties despite the return after a shoulder injury of star hooker Agustin Creevy and they backpedalled several times at the Estadio Padre Ernesto Martearena.
Pollard further extended South Africa's lead with a penalty early in the second half but they suffered a setback when Faf de Klerk was sin-binned in the 48th minute for a series of infringements.