Tregubov played for HC CSKA Moscow from 1951–62, SKA Kuibyshev from 1962–64, and Khimik Voskresensk in 1964-65. He was named to the Soviet all-star team four consecutive years beginning in 1955. He was inducted into the USSR Hall of Fame in 1956.
Tregubov played 100 games for the national team. He played in six IIHF World Championships, being named the best defenceman in 1958 and 1961. He won the 1956 Olympic and World Championship gold in 1956, as well as World Championship silver four times and bronze once.