During the 1950s, along with Ferenc Puskás, Zoltán Czibor, József Bozsik and Nándor Hidegkuti, he was a member of the Mighty Magyars.

He is the joint second most prolific goalscorer in national team matches in all levels in recorded history according to the Rec.Sport.Soccer Statistics Foundation (RSSSF) with 124 goals scored.

His 1.103 goals/game average is ranked No.1 for players past 43 caps in FIFA class-A competition, closely followed by Gerd Müller with 1.097 goals/game (68 goals in 62 games).

Sándor Kocsis registered a national record of seven hat tricks for Hungary, including a four-goal haul against West Germany at the 1954 World Cup.

Together with Ferenc Puskás, Zoltán Czibor, József Bozsik and Nándor Hidegkuti, he formed the offensive nucleus of the Golden Team that went unbeaten for 32 consecutive games.

The Hungarian national team suffered no defeats in Class-A international matches between 4 June 1950 and 4 July 1954, in the 1954 FIFA World Cup Final.

He finished the 1954 World Cup as top goalscorer, scoring 11 goals including two hat tricks, the first of the three players that achieved this.

In the opening game he scored his first hat trick of the tournament against South Korea as Hungary cruised to a 9–0 win.

The players decided against going back to Hungary and arranged for the return with Athletic to be played at the Heysel Stadium in Brussels.

The players summoned their families from Budapest and, despite opposition from FIFA and the Hungarian football authorities, they organised a fundraising tour of Italy, Portugal, Spain and Brazil.

Kocsis spent one season with Young Fellows Zürich before another Hungarian refugee, László Kubala, persuaded him and Zoltán Czibor to join him at FC Barcelona where he became a vital member of the team.

FC Barcelona also reached the final of the European Cup in 1961 and this saw Czibor and Kocsis return to the Wankdorf Stadium in Bern, where in 1954, while playing for Hungary, they had lost the World Cup Final and where, on 23 February 1958, Kocsis had lost 5–1 to BSC Young Boys while playing for Young Fellows Zürich.

He scored twice in the 1959 Copa del Generalísimo final as FC Barcelona defeated Granada CF 4–1.

In 1961, he also played as a guest for Valencia CF and helped them win their own summer trophy, the Trofeo Naranja.