Yury Baulin began to play hockey in 1952 with Spartak Moscow, but in 1953 joined CSKA Moscow, playing there until 1962. He then played with SKA Leningrad (1962-1964) and ended his playing career in 1964-1965 with Torpedo Ust-Kamenogorsk. After his playing career ended, Baulin worked as a hockey coach.
At first he was the head coach of Torpedo Ust-Kamenogorsk, then worked as a coach with Spartak Moscow in 1971-1972, winning a bronze medal at the 1972 Soviet Championships.
After that he was a long-time coach of Yenbek Alma-Ata until his retirement in the late 1980s.