Replacement flyhalf Manie Libbok missed an easy penalty in the dying minutes from close range to gift Los Pumas a narrow 29-28 victory over the Springboks.
Argentina held out to claim the one-point win over the Springboks in Santiago del Estero on Saturday and set up a Rugby Championship title decider in Nelspruit.
A 68th-minute penalty from flyhalf Tomos Albornoz gave Argentina a 29-28 victory, after the home side trailed 17-0 in the opening 15 minutes.
The win sees Argentina keep alive their slim hopes of claiming a first-ever Rugby Championship title, setting up a decider in the return match at the Mbombela Stadium.
The Springboks came away with a losing bonus point and lead Argentina by five log points, so will just need a solitary point from the final-round match to seal the title.
Scorers:
Argentina 29 (26)
Tries: Mateo Carreras, Pablo Matera, Joel Sclavi, Tomas Albornoz
Conversions: Albornoz (3)
Penalty: Albornoz
SA 28 (22)
Try: Aphelele Fassi, Jesse Kriel, Cobus Reinach
Conversions: Handre Pollard (2)
Penalties: Pollard (2), Manie Libbok