Rivera's 1962 "scudetto" victory with Milan under Nereo Rocco enabled the team to qualify for the European Cup in 1962, and earned him a sixth-place finish in that year's "Ballon d'Or". Despite missing out on the Serie A title the following season, Rivera played a key role in helping Milan finally win their first ever European Cup title in 1963, at the age of twenty, defeating Benfica 2–1 in the final. Rivera was in great form during the match, providing two notable assists for José Altafini's goals; he finished the season in double figures once again with 11 goals for Milan in all competitions, while he made 40 appearances throughout the season for both club and country. Milan suffered a defeat in the Intercontinental Cup, however, in a playoff match against Santos following a 6–6 draw on aggregate. For his performances, Rivera was awarded second place in the prestigious Ballon d'Or award that year, which was won by the Russian goalkeeper Lev Yashin. With the departure of Nereo Rocco to Torino, Milan struggled to replicate the same level of success during the next few seasons, missing out on the league title to cross-city rivals Inter in 1965; despite the club's loss of form during this period, Rivera's performances continued to be decisive, as he managed ninth, seventh, and sixteenth placements respectively in the "Ballon d'Or" in 1964, 1965, and 1967, while he helped Milan win the Coppa Italia during the 1966–67 season, finishing the competition as top-scorer, with 7 goals.