Béla Zsitnik took up rowing in 1941 and, after World War II, took his talents international by competing at the 1947 European Championships, where he won gold for Hungary in the coxed pairs alongside Antal Szendey and the non-Olympian Szaniszlo Latinovits. His next stop was the 1948 London Olympics where, with Róbert Zimonyi replacing Latinovits, he captured bronze in the same event. Zsitnik returned to the Olympics in 1952 as a member of the coxed eights, with Zimonyi, István Sándor, Csaba Kovács, Miklós Zágon, Tibor Nádas, Rezső Riheczky, Pál Bakos, and László Marton, where the squad was eliminated in the semi-finals repêchage. After skipping the Melbourne Games, he made his final Olympic appearance in 1960, where he was eliminated in the round one repêchage of the coxless fours, alongside Lajos Kiss, György Sarlós, and József Sátori.
Zsitnik’s career was not over, however, as he won one more national championship and attended the 1961 European Championships before retiring in 1962. He then held a number of administrative positions within the sport, including Secretary General of the national rowing federation from 1967 through 1972. His son Béla Zsitnik, Jr. was a member of Hungary’s coxed eights squad at the 1972 Munich Olympics, where they placed seventh.