János Beszteri-Balogh started his sports career in the Budapest Szikra ice hockey team in 1953 before moving to Ferencváros two years later. He played for the green and whites in two periods (1955-65, 1969-70), winning the Hungarian championship in 1961, 1962, and 1964. He played in the Vörös Meteor team in the 1967/1968 season. He was a technically very skilled player, playing usefully both in attack and defense.
Between 1958 and 1964 Beszteri made 22 appearances for the Hungarian national team. He was a member of the Hungarian national team that participated in the 1964 Winter Olympics in Innsbruck, which is still the last national team that made it to the Winter Games. In the same year he also obtained a coaching qualification.
In 2012 Beszteri was inducted into the Hungarian Ice Hockey Hall of Fame.