Throughout his club career, Pivatelli most notably played for A.C. Milan (1961–63); he also played for Hellas Verona F.C. (1950–53), Bologna F.C. 1909 (1953–60), and S.S.C. Napoli (1960–61). After being dropped from the Inter Youth Side, Pivatelli was acquired by Verona in 1950, with whom he made his Serie B debut at the age of 17, scoring his first professional goal in his second appearance with the club, in a 4–1 victory over Vicenza. The following season, he was promoted to the starting line-up, and scored a total of 25 goals in 68 games for his team during the next three seasons, also helping the struggling club avoid relegation. After joining Bologna in 1953, he made his Serie A debut with the club on 13 September 1953, in a 2–1 home win over Atalanta. With the Emilian side, he was the Serie A top-scorer during the 1955–56 Serie A season, with 29 league goals in 30 appearances, and was the only Italian player to win the Capocannoniere title during the 1950s. In total, he scored 105 goals for Bologna during his seven seasons with the club. After playing with Napoli for the 1960–61 season, he joined Milan in 1961, and was part of the side that won the Serie A title in 1962, and the European Cup in 1963 under manager Nereo Rocco, after which he subsequently retired from playing professional football.