As a high school senior in Texas, Morrow won 17 consecutive 100- and 220-yard dashes and state titles in both events. In 1955, while a freshman at Abilene Christian University, Morrow made his debut in national competition by winning the 100-yard dash at the Amateur Athletic Union championships. At the 1956 National Collegiate Athletic Association championships, Morrow won both the 100- and 200-metre dashes. Morrow's time of 20.6 sec in the 200 metres equaled the best ever on a course with a full turn.

At the 1956 Olympics in Melbourne, Morrow went through the 100-metres series without losing a race, pulling away from American Thane Baker in the final. Despite running with a bandaged thigh in the 200-metre dash, Morrow set an Olympic record (20.6 sec) while capturing his second gold medal. In the 4  × 100-metre relay, Morrow's teammates, Ira Murchison, Leamon King, and Baker, gave him a narrow lead over the Soviets, which Morrow extended. Their time (39.5 sec) broke a world record that had endured for 20 years. With that victory, Morrow became the first track performer since American Jesse Owens in 1936 to win gold medals in the 100- and 200-metre dashes and the 4  × 100-metre relay.

Between 1956 and 1958 Morrow ranked as the top sprinter in the world, equaling world records in the 100- and 220-yard dashes and winning all the major championship titles for which he competed. He was elected to the National Track and Field Hall of Fame in 1975.