Los Pumas defeated the Springboks 26-24, securing their first home win over South Africa since their first meeting in South America 23 years ago.
The previous 11 results had seen one draw and ten losses for Argentina.
South Africa remain in third despite the defeat, behind New Zealand in first and England in second.
Australia, Wales and Ireland are in fourth, fifth and sixth while Los Pumas are now in seventh place ahead of France in eighth and Scotland in ninth.
Fiji remain in tenth place, just under five points adrift of Scotland.
The Scottish Rugby Union recently announced that Glasgow Warriors head coach Gregor Townsend will succeed Vern Cotter as the national team coach in June 2017.