During the late 1950s and '60s Antonio Angelillo, Omar Sivori and Maschio acquired the nickname The Angels with Dirty Faces when they moved en masse to Italy. The name, an ironic reference to the then-celebrated Angels with Dirty Faces movie, was given to them on account of their typically South American colour and flair. They were also known as The Trio of Death because of their clinical ability in scoring goals.
Maschio started playing at Arsenal de Llavallol to later move to Quilmes Atlético Club where he proved himself a prolific goal-scorer. He joined Racing Club in 1954, and transferred to Italy in 1957. He had been linked with a move to Juventus in 1956, but their interest cooled following the international between Italy and Argentina in Buenos Aires that year when he looked ineffective. Instead he signed for Bologna in 1957, but although he paired up with Bernard Vukas there, he was unable to recreate the form he showed at Racing.
From Bologna Maschio moved to Atalanta who bought a half-share in him during the 1959-60 season. In Bergamo Maschio regained the form that had taken him to international prominence scoring heavily, and creating numerous chances for his colleagues. At Atalanta Maschio moved from playing as central striker to a deeper role which allowed him to use his vision and creativity. So impressive was his form at Atalanta that he moved to Inter in 1962. However, Maschio failed to fit in with manager Helenio Herrera who used him as a central striker and his time in Milan was of limited success. Following his time at Inter, Maschio briefly played with Fiorentina.