In hockey, Baliuk played from 1954 to 1964 in the Ontario Hockey Association, Quebec Hockey League, Western Hockey League, American Hockey League, and National Hockey League. He won the Dudley "Red" Garrett Memorial Award as Rookie of the Year while playing with the Providence Reds of the AHL in 1959-60. He played in 7 games for the Boston Bruins in the NHL during the 1959-60 season.