Dezső Fábián was a swimmer and water polo player for the MAC from 1936 to 1945, winning Hungarian championship titles in both disciplines. As a swimmer he became the Hungarian youth champion in the 200 metres breaststroke in 1936. The following year he became the senior champion in the same event. In the 1940s he won four more championships in breaststroke and the relay. He also swam for the national swimming team six times. After World War II he became a water polo player for the UTE, and from 1948 for the FTC. He won his only water polo championship title in 1946.
Between 1944 and 1952 Fábián played for the Hungarian national water polo team twenty-five times. He was a member of the Hungarian team that won the silver medal at the 1948 London Olympics and gold at the 1952 Helsinki Olympics. In an important match against the Italians in London, he failed to convert the four-metre penalty awarded in the last moments. Thus, the team “only” came second. In Helsinki he only got a chance to play in one match in the team that won the championship. After his retirement he trained the FTC youth team and then led the senior team to the championship four times in the first half of the 1960s. From 1970 he worked as a coach of the OSC youth team. In November 1965 he was appointed as the secretary of the water polo committee of the Hungarian Swimming Association.