As a collegian, Burleson teamed with superstar David Thompson, guard Monte Towe and forward Tim Stoddard (who would go on to have success as a Major League Baseballpitcher) to dethrone UCLA and win the 1974 NCAA Championship. Burleson was the MVP of the 1973 and 1974 ACC Tournaments and was All-Final Four in 1974. Burleson's defense of UCLA superstar Bill Walton was key to the Wolfpack's semifinal win. He was a member of the 1973 World University Games Gold Medal basketball team.
When Burleson was recruited he was officially measured at 7′2″ tall, but the coaching staff at North Carolina State decided to list him at 7′4″. Burleson wanted to be listed at his actual height but the coaching staff said he would officially be the tallest player in American basketball and it would bring a lot of good exposure to him and the school.
Burleson was also a member of the 1972 U.S. Olympic Basketball Team that lost an epic and controversial gold medal game to the Soviet Union. The entire 1972 Olympic Basketball team believed they had been cheated and voted unanimously to not accept the silver.
Drafted by the Seattle SuperSonics as the third overall player in the 1974 NBA Draft, Burleson was named to the 1974-75 NBA All-Rookie Team. Playing under coach Bill Russell, Burleson recorded strong playoff performances in both 1975 and 1976 for Seattle. For his playoff career, Burleson averaged over 20 points, 10 rebounds, and two blocks per game. His second season as a professional proved to be his best, as he averaged 15.6 points, 9.0 rebounds, and 1.8 blocks per game. Just as he began to dominate the NBA game, he was injured breaking up a fight between his teammate and an opposing team member. The injury was instrumental in his steady decline over the next several years.
Burleson was known throughout his amateur and pro career as a good shot blocker. He played eight seasons in the NBA with three different teams (Seattle, the Kansas City Kings and the Atlanta Hawks). He currently lives in Avery County, North Carolina with his wife Denise. They have three sons: Robert, David, and Quentin. He is an avid supporter of North Carolina State University.