Brunson graduated from Temple University. He was signed as a free agent by the Orlando Magic in 1997, he played for the New York Knicks and the Portland Trail Blazers during that season. He then played for the Knicks for the 1999 season. He then played for the Trail Blazers, Boston Celtics, Knicks during the 2000 season. He again played for the Trail Blazers for the 2001 season. Then he signed with the Chicago Bulls for the 2002 season. He then played for the Toronto Raptors and the Chicago Bulls for the 2003 season before moving on to the Los Angeles Clippers in 2004-05. A breakout season landed him a 2005-06 contract with the Seattle Supersonics, but he played only four games due to injury throughout most of the season. On February 28, 2006, the Sonics waived Brunson. He was subsequently signed by the Houston Rockets.
He has been known by the nickname The Brunson Burner.