Argentina have won successive Tests against France for the first time since their 2007 Rugby World Cup breakthrough when they took the home series opener 30-19.
The Pumas won the previous Test in Paris in 2014.
France couldn't choose internationals from the national club semi-finals this weekend.
But after Clermont and Montpellier lost, their players can be summoned by France to Tucuman again for the second Test next weekend, when the Top 14 final will be contested by Toulon and Racing 92.
Argentina led 17-3 after half an hour on Sunday then lost their composure over the next half hour.
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An understrength France team pulled ahead 19-17, and had all of the momentum until prop Jefferson Poirot was sin-binned for a deliberate knockdown.
Nicolas Sanchez's penalty kick put the Pumas back in front, they stopped their carelessness, and pulled away, making the result safe with a try from a 50m gallop by lock Guido Petti seven minutes from the end.
Argentina made two changes, in the forwards, and resumed where they left off from beating Italy 30-24 in Santa Fe the previous weekend.
They pinched French ball in a tackle, counter-attacked from 70m out, and 10 phases later centre Matias Moroni sent winger Manuel Montero untouched into the left corner.
Soon after, Montero stepped one defender, stiff-armed another, and one-hand passed out of a French crowd to send fullback Joaquin Tuculet streaking to the opposite corner.
The Pumas were playing like the French of old.
The French replied with a try of the old Pumas - a 10m rolling maul, finished by hooker Remi Bonfils, one of seven starting new caps.
