Centre Felipe Contepomi kicked 13 points with three penalties and two conversions.
It was Argentina's second consecutive victory in the June test window after they beat Italy in San Juan last weekend. They meet France again in Tucuman next Saturday.
The home side, having conceded an early penalty kicked by France scrumhalf Morgan Parra, went 7-3 up with the try by Agulla and captain Contepomi's first conversion.
However, number eight Louis Picamoles went over for France close to the half-hour mark and two more Parra penalties helped the visiting side go in 14-13 ahead at halftime.
Further penalties from Parra and flyhalf Francois Trinh-Duc to one from Contepomi had the French leading 20-16 but they were unable to take advantage when Pumas number eight Tomas Leonardi went to the sin bin.
With four minutes left and France enjoying the lions share of possession, Contepomi recovered the ball in defence, centre Joaquin Tuculet kicked ahead and Montero chased for a try with the captain converting.