In 1967 he started professional ice hockey career playing for HC České Budějovice Junior team and from 1970 became a member of 'senior team'. In the same year Dvořák was named the best defender of World Junior Ice Hockey Championships held in Sweden. During his military service he moved to the army team Dukla Jihlava where he spent 2 seasons. He also played for Czechoslovak national ice hockey team and won 8 medals overall in the Ice Hockey World Championships in years 1974, 1975, 1976, 1977, 1978, 1982 and 1983 and represented Czechoslovakia on 1976 and 1981 Canada Cups and on 1980 Winter Olympics as well. He was drafted by Philadelphia Flyers in the 3rd round in 1982 and played 3 seasons in North America, playing in the NHL for Philadelphia. He had to wait until his thirties to play NHL, as playing overseas under the age of 30 was strictly prohibited because of sports rules during communism era in Czechoslovakia. He left professional ice hockey after the 88-89 season and went back to Czechoslovakia to play for HC České Budějovice.