During the first three seasons of his career (1954–1956), the Eskimos won consecutive Grey Cups. In the 1954 Grey Cup, Parker made one of the most famous plays in Grey Cup history when, in the fourth quarter, Ted Tully hit Montreal Alouettes running back Chuck Hunsinger forcing a fumble. Parker recovered the ball and returned it 90 yards for a touchdown, giving the Eskimos, who were a large underdog in the game, a surprise victory. Parker's 90-yard fumble return remained a Grey Cup record until Cassius Vaughn's 109 yard fumble return in the 105th Grey Cup.