Angelillo, along with his countrymen Omar Sivori and Humberto Maschio acquired the nickname "the Angels with Dirty Faces" when they moved to Italy in the latter part of the 1950's on account of their typically South American colour and flair. They were also known as ‘The Trio of Death’ because of their clinical finishing.
From 1957 to 1961, Angelillo played 127 games with Internazionale, scoring 77 times. In Serie A, he appeared in 113 matches and scored 68 goals for Internazionale.
In the 1958/59 season, Angelillo scored 33 goals in 33 matches, being the tournament's top scorer. His goal total was the highest since Gunnar Nordahl had scored 34 in the 1950/51 season, and no player since has scored as many goals in a Serie A season.
Although Angelillo was Inter's highest goalscorer while he was playing there, he did not win any titles with the Nerazurri.
From 1961 to 1965, Angelillo played 106 games with AS Roma in Serie A, scoring 27 times. He then spent one season at AC Milan, scoring one goal in 11 matches. The following year, he signed with Calcio Lecco 1912, playing 12 matches and scoring one goal, with the team being relegated to Serie B. He remained in Serie B, where his next and last team was Genoa.
After retiring from playing, he stayed living in Italy, where he became a coach, managing several lower division clubs.