The win was just reward for an Argentina side angry with themselves for letting victory slip from their grasp in Nelspruit in their tournament opener and vowing they would beat the Springboks at home for a first time.
"We played a fantastic first half, we had a lead that wasn't a true reflection of what we saw on the pitch," Argentina coach Daniel Hourcade told reporters.
"In the second half they came at us and we started to have problems with injuries... The truth is this team showed enormous heart in adversity today. I'm really happy because I think we deserved to win it."
Under new coach Allister Coetzee, South Africa have lost two of their five tests this year but the strength in depth of the Springboks squad very nearly saved the day in Argentina.
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They may also be concerned that having won 18 and drawn one of their first 19 meetings with Argentina, they have now lost two of the last five.
It was Argentina's third win in the championship since joining the elite southern hemisphere tournament in 2015, having also beaten Australia once.
EARLY DOMINANCE
Argentina dominated the first half despite losing prop Ramiro Herrera to the sin bin for a bad tackle in the 20th minute, taking a 6-3 lead while down to 14 men with flyhalf Nicolas Sanchez's second penalty.
The Pumas added a try as soon as Herrera had rejoined the fray, when a sweeping passing movement from inside their 22 ended with fullback Joaquin Tuculet touching down to put them 13-3 ahead at the interval.
South Africa began the second half with purpose and an attack down the left brought their first try after flanker Francois Louw's slick pass to Bryan Habana sent the winger away for a record 65th test try and 20th in the championship.
Fullback Johan Goosen converted to level the score at 13-13 and Sanchez, who took a nasty knock to the head trying to defend the attack, had to be replaced with centre Juan Martin Hernandez moving inside to take his place.
Hernandez, who masterminded Argentina's win in Durban last year, engineered a fine second Pumas try with a neat crossfield kick to the far right corner, where flanker Juan Leguizamon beat Habana to the high ball and scored.
Argentina were seven points ahead with 13 minutes remaining but lost Hernandez to injury and South Africa edged to within two when replacement forward Pieter-Steph du Toit went over from a scrum close to the line.
Morne Steyn, who had come off the bench looking to bolster South Africa with his place kicking from long distance, guided the visitors into a one-point lead going into the last six minutes when he landed the second of his penalties.
However, strong defending by Argentina and the 40-metre penalty from a cool-headed Gonzalez Iglesias allowed the Pumas to snatch a hard-earned victory.
(Editing by John O'Brien)
