José Durañona first gained attention for his swimming talents during World War II, when he set a South American record in the 300 metres freestyle in 1940. He won numerous Argentine domestic freestyle titles during the 1940s and notched several victories at the 1941 and 1946 South American Championships. The pinnacle of his career came when he was selected for the 1948 London Olympics. There, he placed sixth in the 4x200 metres freestyle relay (with Horacio White, Juan Garay, Alfredo Yantorno, and Augusto Cantón) and was eliminated in round one of the 400 metres freestyle. He retired from active competition shortly after the Games.