Argentina ended South Africa's unbeaten run with a thrilling 29-28 win in their Rugby Championship match at Estadio Unico Madre de Ciudades on Saturday.
Replacement fly-half Manie Libbok missed a penalty goal attempt from 35 metres in the last minute which would have secured the title for South Africa, who had won their four previous matches.
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The Springboks remain favourites to win the championship but Argentina gave themselves an outside chance of lifting the crown for the first time.
They will have to beat South Africa with a bonus point in a return match in Mbombela next Saturday and prevent the Springboks securing any points.
"Credit to Argentina, they put us under a lot of pressure," said Salmaan Moerat, standing in for regular Springbok captain Siya Kolisi, who was rested.
"For large parts of the game we played good rugby but they pulled it through."
An Argentine win seemed unlikely when the Springboks made a blazing start in a match played in 36 degrees Celsius (97 Fahrenheit) heat, leading 17-0 inside 13 minutes.
South Africa won a penalty when they pushed their opponents off the ball in the first scrum. Fly-half Handre Pollard kicked for touch to set up a line-out and full-back Aphelele Fassi was put into a gap to score a fourth-minute try.
Centre Jesse Kriel added another try and Pollard kicked the conversion and a penalty as South Africa seemed to take control.
But Argentina hit back in spectacular fashion, with wing Mateo Carreras reducing the deficit two minutes later.
The match changed dramatically when Springbok wing Kurt-Lee Arendse was sent to the sin bin for a dangerous tackle.
Flanker Pablo Matera and prop Joel Sclavi scored tries while Arendse was off the field and fly-half Tomas Albornoz added a fourth for Argentina to lead 26-17.
Scrum-half Cobus Reinach scored a try for the Springboks shortly before the end of a frenetic first half with Argentina leading 26-22 at the break.
South African coach Rassie Erasmus had made 10 changes from the team that beat New Zealand 18-12 in Cape Town two weeks ago and the normally well-organised Springbok defence proved vulnerable against the hard-running, slick-handling Pumas.
South Africa had conceded only five tries in winning their first four matches in the southern hemisphere championship.
Penalties by Pollard and Libbok put South Africa ahead as the pace of the match slowed in the second half.
Lock Eben Etzebeth won a South African record-equalling 127th Test cap when the Springboks refreshed their forwards with their customary "bomb squad of replacements early in the second half.
With the South Africans dominating the scrums, the visitors seemed to have regained control but a run by Albornoz took the Pumas deep into South African territory with 11 minutes remaining and the fly-half put his side back in front when they were awarded a penalty.
It all came down to Libbok at the end, but he pulled his kick left of the posts.
