Moore was chosen by the Miami Dolphins in the third round (78th pick overall) of the 1974 NFL Draft, and he played for the Dolphins for 13 seasons from to . He was elected to the Pro Bowl in , after a season in which he made 52 receptions and led the league with 12 receiving touchdowns (he also had a rushing touchdown that year). Moore is immortalized in the famous "Helicopter Catch" video clip—while making a reception against the New York Jets in Giants Stadium in , he was hit simultaneously from opposite directions by two Jets tacklers sending his body spinning into the air. The catch was a crucial third-down conversion, leading to a score and a come-from-behind win in a closely contested divisional game.