Burton was the Boston Patriots' first-ever American Football League draft choice in 1960. He was the first Patriot to rush for over 100 yards: 127 against the Denver Broncos on October 23, 1960, as well as numerous other firsts for the Patriots. His 91-yard touchdown return on a missed field goal in 1962 remains a Patriot record. He compiled 1,009 combined yards in rushing and receiving in 1962, and provided strong depth at running back for the Patriots from 1960 through 1965.