Alberto "Don Padilla" Zozaya started his career in the early 1930s with Estudiantes. He was the first player to score a goal in the professional era of Argentine football, which began in 1931.
Zozaya became an integral part of the Estudiantes team of the 1930s nicknamed "Los Profesores" (The Professors). In 1931 he scored 33 goals in the league to become the top scorer in the Primera División Argentina and the whole of South America.
In 1939 Zozaya moved to Racing Club de Avellaneda but he only played 2 games before moving to Bella Vista in Uruguay but he did not settle there either and retired at the end of the 1940 season.
After retiring as a player Zozaya went into management, he was manager of Portuguese side Benfica from 1952 to 1953. He was also manager of Gimnasia de La Plata.