The Cleveland Browns selected Parrish in the ninth round (108th pick overall) of the 1958 NFL Draft, and he played for the Browns from to . Memorably, he returned one interception for 92 yards and a touchdown in 1960, and intercepted a pass from the great Y. A. Tittle in his last game in 1964 (Tittle himself had to tackle Parrish to keep him from scoring). Parrish was a key man of the Browns' defense on their run to winning the 1964 NFL championship. In his seven seasons with the Browns, he had 29 interceptions, including three returned for touchdowns. After playing in one game of the season, Parrish requested that he be released because the Browns asked him to share time at his position with another player, and played the balance of the 1966 season (11 games) for the Houston Oilers of the AFL before retiring at season's end.