Nicknamed "La Gloria", Tesoriere soon gained the attention of media and fans for his skills and good performances, being called up for the Argentina national team in 1920. With Argentina he played the 1921 and 1921 Copa América (then called "Campeonato Sudamericano"), keeping his goal unbeaten in both occasions. At the end of the Argentina v. Uruguay match for the 1924 South American Championship, Tesoriere was carried aloft by the Uruguayan supporters as a recognition for his outstanding performance during the game. The crowd said to President of Uruguay, José Serrato (who had attended the match): "Sir, this man did not allow us to defeat the Argentine team".