At international level, he represented Italy 60 times between 1962 and 1974, scoring 14 goals, and took part at four World Cups (1962, 1966, 1970, and 1974). Rivera is widely remembered for scoring the decisive goal in Italy's 4–3 extra-time win over West Germany in the semi-final of the 1970 World Cup, leading the team to final, only to suffer a 4–1 defeat against Brazil, however. Rivera was also a member of the first Italian side ever to win the European Football Championship in 1968, on home soil, and represented Italy at the 1960 Summer Olympics in Rome, helping the team to a fourth-place finish.