Nasazzi is regarded by many as Uruguay's greatest ever football player. He was known as 'El Gran Mariscal' (The Great Marshal) and had already won the gold medal at the 1924 and 1928 Olympic Games, as well as the Copa América in 1923, 1924 and 1926, by the time of the first World Cup.
During the World Cup tournament, Uruguay's only serious rivals were Argentina. After defeating Peru and Romania in the first round, Uruguay defeated the Yugoslavia 6-1 in the semi-finals to set up a final against Argentina. Although his team were 2-1 behind at half-time, Nasazzi rallied his teammates in the second half, leading them to a famous 4-2 victory and making himself the first captain to lift the Jules Rimet Trophy.
Although Uruguay refused to defend their title in 1934, Nasazzi did win the Copa América again (in 1935), before retiring in 1937.
Nasazzi's Baton is an unofficial title named after José. It is said to have been held by Uruguay after the first World Cup, and subsequently to have been taken over by any team to beat the holders over 90 minutes in a competitive match. It is currently held by Hungary.