France were denied a record ninth straight win as they slumped to a first-ever defeat in Marseille.
Durand set Argentina on their way with a first-half try
Argentina scored two tries with Martin Durand and Omar Hasan both crossing and Felipe Contepomi kicking 14 points to secure a famous scalp.
Tony Marsh scored a try for France, who had beaten Australia last week, but the hosts could not recover from a 19-5 half-time deficit.
Hasan's late try clinched the Pumas' fourth win in a row against the French.
France coach Bernard Laporte admitted the better team had won.
"They were superior in every section of play - going forward and with their kicking," he said.
"They beat the best we had to offer, which proves that they are now a major rugby nation."
His Argentine counterpart Marcelo Loffreda was understandably proud of his side.
"This was a totally deserved victory," he said.
"We more than matched them both physically and mentally and against a side that easily beat Australia."
Laporte indicated he would look to make changes ahead of next week's match against New Zealand at the Stade de France.
"We did not do much right," he added. "We could have played 10 times better. We'll have to analyze it and look at certain players."
France seem certain to recall South African-born duo Pieter de Villiers and Brian Liebenberg for next weekend's game.
But they have doubts over full-back Nicolas Brusque, who went off at half-time against Argentina with badly cut knees.
Winger Cedric Heymans was due to have a scan on a painful right ankle, while scrum-half Jean-Baptiste Elissalde, went off after a blow to his pelvis.
France: Brusque, Rougerie, Marsh, Jauzion, Heymans; Michalak, Elissalde; Milloud, Servat, Marconnet, Thion, Pelous, Betsen, Magne, Harinordoquy.
Replacements: Bruno, Mas, Pape, Bonnaire, Peyrelongue, Poitrenaud, Dominici.
Argentina: Hernandez, Borges, Martin Aramburu, M Contepomi, Senillosa; F Contepomi, Pichot; Roncero, Ledesma, Hasan,Albacete, Alvarez-Kairelis, Ostiglia, Durand, Longo.
Replacements: Mendez, Rodriguez, Bouza, Schusterman, N Fernandez Miranda, De la Cruz, J Fernandez Miranda.
Referee: J Kaplan (South Africa)