The product of West Texas State was used mostly as a returner in his early seasons, and as a rookie in 1969, he led the league in Kick Return Yards (1,136) and Return Yards (1,308).  Morris would slowly see more work as a Running Back and would go to the Pro Bowl three years in a row (1971 to 1973).  In 1972, he finished the year with an even 1,000 Rushing Yards with a league-leading 12 Touchdowns from the ground.  That was the year where the Dolphins went undefeated and won their first Super Bowl.

Morris and the Dolphins won the Super Bowl again in 1973, with the Running Back going for 954 Yards and 10 TDs.  That year he would finish first in Yards per Attempt.  Morris was injured through most of 1974, and while he had a comeback in 1975 with 875 Yards from the ground, he was traded to the San Diego Chargers afterward.

With Miami, Morris had 7,794 All-Purpose Yards.