Morrow won the 100m, 200m and 4x100m relay in Melbourne, becoming the first man since fellow American Jesse Owens (1936) to do the sprint treble.
He broke Owens' Olympic record in the 200m before anchoring the USA to a new 4x100m record.
From farmboy to fastest man in the world
Born in Harlingen in October 1935, Bobby Joe Morrow was raised by his parents on a cotton and carrot farm in San Benito.
A standout American footballer and then sprinter at the local high school, he turned down approaches from top universities across the country to stay at home in Texas.
'The San Benito Bullet' went to Abilene Christian College (now University) where coach Oliver Jackson taught him how to relax during races.
As one writer put it, "He doesn’t appear especially to pull, push, or drive as he runs. He’s never struggling... he’s like a wheel rolling down the track."
Morrow's times were often met with scepticism by those outside Texas who believed that the state's track meetings had strong winds favouring the sprinters.
He answered those questions emphatically at the Olympic Trials in Los Angeles, cruising to victory over 100m and 200m, before doing the same in Melbourne despite being weakened by a virus just days before.
His three Olympic golds in Australia propelled him to stardom with Morrow gracing the cover of Life magazine and Sports Illustrated, beating baseball great Mickey Mantle to the latter's Sportsman of the Year award.
Morrow told Texas Monthly in 1984, "To be able to represent your country in the Olympic Games is an experience an athlete will never forget."
But he did not enjoy what followed saying, "I have shunned publicity rather than sought it out. I like for people to know me for what I am, not what I’ve done.
"The U.S. Chamber of Commerce named me one of the nine Great Living Americans. Just because I went to the Olympic Games and had the natural ability that my mother probably gave me through birth, why should I be named one of the nine Great Living Americans? Just because of my legs.”
While he was the outstanding performer on the day, there was another man who would become even more of a household name on the bill with future NBA legend Wilt Chamberlain tying for first in the high jump.
Morrow's amateur status left him largely unable to cash in on his fame and, with twin children to support, he took a vice-presidential post with the Abilene Bank of Commerce in 1959 which allowed him to take part in invitational meets.
His hopes of retaining his Olympic title at Rome 1960 were wrecked by a thigh injury sustained at the Meet of Champions in Houston.
He recovered to compete in the trials but finished fourth in the 200m, missing out by one spot.
Morrow says he was invited to train with the squad in California for six weeks having been told he would go to Rome if he showed improvement.
Having left his job in Abilene, he told Texas Monthly in 1984, "My leg was healing, and I was beating the ones who had made the team, so the coaches and officials had a meeting; they were supposed to leave for the Olympics the next morning. I called and they said, 'We haven’t made a decision yet. Come to the plane in the morning and we’ll tell you then.' So I got out to the airport, and they said, ‘Nope, you’re not going.'"
He retired after that apparent snub and, while being left out of the squad diminished his national appeal, he was still a big draw in Texas known for his integrity as well as his sporting prowess.
However, Morrow soon became unwittingly involved in unscrupulous businesses leading to the collapse of his marriage.
He later remarried before returning to San Benito in the early 1970s to take over the running of the family farm where he lived until his passing.
Morrow was inducted into the USA Track and Field Hall of Fame in 1989 and San Benito High School named its new 11,000-seater football stadium in 2006 the Bobby Morrow Stadium.