The match had looked like ending in a perfect home debut for the Pumas, famously tough opponents on Argentine soil long before their entry into their first annual major tournament.
Argentina dominated a first half in which the Springboks, who had beaten them 27-6 at home last weekend, were given little chance to display the running strengths they have honed in Super 15 rugby.
South Africa's coach Heyneke Meyer pointed to the difficulty his players had endured with Argentina's more classical Test game, played tight and close to the forwards.
"We had a lot of youngsters in the team, with not all that much experience, but it's not an excuse. Technically we weren't good enough at the breakdown," he said.
"We can play much better. These players are more used to Super 15 rugby. The Pumas play a European game.
"I'm sorry the way we played didn't honour the great welcome we have had in Mendoza. The people here can be proud of their team."
Springboks captain and centre Jean de Villiers said: "It was a very frustrating game for the outside backs, we didn't get too much ball.
The factor which made the match all the more frustrating for South Africa was Argentina's marked improvement on their tournament debut in Cape Town.
"We talked all week about improving how we got out of our half and for a big part of the match we did that well," Pumas captain Juan Fernandez Lobbe said.
"The key was our attitude, confidence and giving our all. We've progressed from last week and now we face the biggest challenges we'll have as players," he said in a reference to the forthcoming away matches against the All Blacks and the Wallabies.
Argentina coach Santiago Phelan added: "We had hoped for another result, a winning game but we are still very satisfied. We did a lot of work [on the breakdown], I think it's a strength of Argentine rugby."
The Pumas, who had lost their previous 14 matches against South Africa, ran up a 13-3 halftime lead after a early try by centre Santiago Fernandez.
Several phases of attack ended when they broke through the middle of the Springboks defence and prop Juan Figallo handed the final pass to Fernandez who ran in under the posts.
Fullback Martin Rodriguez converted and finished with a tally of 11 points including three penalties, exactly the same as flyhalf Steyn.
Argentina, though, were left to rue the kick out of defence by Fernandez that was charged down by his opposite number Frans Steyn, who chased the ball and scored the Springboks' try 15 minutes from time.
The error would have cost Argentina more dearly had Steyn slotted over a late penalty from out on the right wing. – Reuters