Dillon started out with the Springfield Indians of the Canadian-American Hockey League from 1928 to 1931. In the middle of the 1930-31 season he was called up to the New York Rangers. He remained with the Rangers for eight more full seasons, never missing a single game. Dillon was a second All-Star in 1935-36 and 1936-37 and a first All-Star in 1937-38. His NHL rights were sold to the Detroit Red Wings in 1939 and he played one season there. After that he was traded to the Providence Reds of the American Hockey League (AHL).