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.

[6] Rivera was an elegant, efficient, and creative offensive playmaker, with an eye for goal, who possessed excellent vision and technical ability, and who was highly regarded for his footballing intelligence, leadership, correct behaviour, and class.

In 2013, he was appointed as President of the educational youth sector for the Italy national team by the FIGC, along with Roberto Baggio and Arrigo Sacchi, under head coach Cesare Prandelli.

Nicknamed l'Abatino, and the Golden Boy of Italian football throughout his career,[1][2][22][23][24] Rivera was the product of his hometown club's youth football academy; he joined the first team in 1958 and made his debut in Serie A for the Alessandria senior side against Internazionale on 2 June 1959 at the age of only fifteen years, nine months and fifteen days, in a 1–1 draw; later that year, he scored his first Serie A goal in a 2–2 home draw with Sampdoria on 25 October.

[1][7][8][27][28] Rivera's final appearance with Alessandria came on 19 June 1960, in a 2–0 home defeat against FC La Chaux-de-Fonds in the first-ever edition of the Coppa delle Alpi.

[1][2][8][9][22][30][31] Due to his performances throughout the season, on 13 May 1962, aged just eighteen, Rivera played his first competitive match for the Italy national team at that year's World Cup in Chile.

[1][2][8][22][23][33] 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.

[1][7][8][9] 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.

Rivera picked up a three-month suspension because of his statements against Italian referees, suggesting that they favoured Milan's rivals Inter and Juventus; coincidentally, the latter team won the Serie A title that season.

[1][7][9][33] Rivera finished the 1972–73 season as top-scorer in Serie A alongside Paolo Pulici and Giuseppe Savoldi, with 17 goals in 28 league matches, and scored a personal best of 20 goals in all club competitions, as, despite winning both the Coppa Italia and the Cup Winners' Cup, Milan once again finished in second place in the league, narrowly missing out on the Serie A title to Juventus, after infamously losing out against Verona on the final matchday of the season.

Rivera made his international debut with the under-21 side on 9 March 1960, scoring 2 goals in a 4–1 pre-Olympic friendly win over Switzerland, alongside Giacomo Bulgarelli.

At the Summer Olympics in Rome, Rivera made his tournament debut in a 4–1 win against Taiwan, at the age of seventeen, and teamed up with Bulgarelli in midfield to help the Italians to a fourth-place finish under Viani, scoring three goals in five matches.

[37] Despite Rivera's creative talent, offensive capabilities, and technical skills, the celebrated Italian sports journalist Gianni Brera was critical of the youngster's performance, due to his lack of pace, physicality, and his poor defensive work-rate, nicknaming him l'Abatino (the little abbot), and also stating that the in-form Angelo Sormani should have played in his place.

At the prime of his career, much was expected of him throughout the tournament; after a slow start, his excellent form in the knock-out stages saw him become Italy's star player throughout the competition, as they reached the final, only to lose out 4–1 to a Pelé-led Brazil side.

Although Rivera was arguably the more famous of the two stars at the time, as the reigning European Footballer of the Year, Valcareggi elected to start Mazzola, due to his pace, stamina, superior work rate, and stronger physical and athletic attributes, which he deemed more important in the tournament, and Rivera missed out on Italy's opening two group matches, with his absence being blamed on "stomach troubles"; he made his first appearance of the tournament in Italy's final group match, a 0–0 draw against Israel on 11 June, coming on for Angelo Domenghini.

Due to Rivera's frequent arguments with the Italian coaching staff over his limited playing time, his mentor Rocco had to be flown in to prevent him from leaving the squad.

Although Rivera's playing style involved less running, physicality, tactical discipline, and work off the ball than Mazzola's, and made Italy less compact and more vulnerable defensively, it also allowed his team to control possession in midfield, due to Rivera's ability to dictate the play with his passing moves, provide accurate long passes, and create more chances for the team's strikers.

When Mazzola came down with a stomach flu, and struggled to regain full match fitness for the knock-out round, Valcareggi therefore devised a controversial solution to play both players and get the best out of their abilities: the quicker and more hard-working Mazzola would start in the first half, while Rivera would come on at halftime, when the opposing teams would begin to tire, and the tempo of the game had slowed down, giving him more time to orchestrate goal scoring opportunities; this strategy was later dubbed the "staffetta" (relay).

Although the two creative Italian stars Rivera and Mazzola were finally able to play alongside each other, it was too late to overturn the result, and Brazil won the match 4–1 to capture the title.

The 1974 World Cup elimination marked the end of Rivera's international career; his last appearance with Italy came in the team's second group fixture, a 1–1 draw against Argentina, on 19 June.

[8][62] "Yes, he doesn't run a lot, but if I want good football, creativity, the art of turning around a situation from the first to the ninetieth minute, only Rivera can give me all of this with his flashes.

Despite his notable skill, technical ability, and elegance on the ball, Rivera would often avoid challenging defenders gratuitously in one on one situations, making unnecessary flashy moves or plays, or undertaking individual dribbling runs, in particular in his later career, unless he deemed them necessary; as such, he was known to be an efficient player, who preferred instead to create space and chances for his team through his precise passing game and offensive movement.

[1][24][32][44][68][63][65] Indeed, above all, Rivera was known for his excellent vision, ability to interpret the game, and his sublime range of passing, which allowed him to control the game and dictate the tempo his team's play in midfield with short exchanges, spread long passes across the pitch, or even play the ball first time, and also made him an excellent assist provider from any position on the field, with either foot;[1][7][24][30][44][63][69][70] in 2011, former playmaker and UEFA president Michel Platini described Rivera as one of the greatest passers in the history of the sport.

[7][8][9][23][33] In addition to his footballing ability, Rivera was also highly regarded throughout his career for his composure under pressure, his correct behaviour on the pitch, longevity, and his vocal leadership, although his outspoken personality also led him to be involved in several controversial clashes with managers, officials, and the media.