He was a football captain at Stanford, leading the NCAA in receptions with 61 in 1959. The following year, he was a first round draft pick of the Dallas Texans. He led the Texans/Chiefs in pass receptions in four seasons (1961–63 and 1965). An AFL All-Star in 1961, he followed that performance with a team-record 12 receptions for touchdowns in 1962. By the end of his career he was the Chiefs all-time reception leader (391) with 5,505 yards and 55 touchdowns.
Teaming with Hall of FamerLen Dawson, Burford was a clutch receiver when the game was on the line and the ball had to be moved forward for a needed first down or for field goal position. For most of his AFL career, Burford was in the top ten in receiving catches, yards, and touchdowns. Burford is a 1975 inductee of the Chiefs' Hall of Fame. In 2010 he was inducted into the African-American Ethnic Sports Hall of Fame. Burford, who is white, was nominated by former black teammate Abner Haynes.