Underwood played as a guard for Hardin-Simmons University during his freshman year from 1982 to 1983 and later transferred to Independence Community College. During his sophomore year, Underwood averaged 17 points a game and led Independence to a second place finish in the NJCAA Men's Division I Basketball Championship game. As a sophomore at Independence, Underwood took a recruiting visit to Oklahoma State University where Bill Self, then an Oklahoma State basketball player, was his host. Days later, Underwood decided to attend Kansas State University, where he would play under head coach Jack Hartman.
Underwood began his coaching career as a graduate assistant at Hardin-Simmons during the 1986–87 campaign. He continued his coaching career as the head coach of Dodge City Community College, where he led the Conquistadors to a 62–60 record from 1988 to 1993. In 1993, he joined Jim Kerwin's staff at Western Illinois, with whom he spent 10 years as an assistant. He led Daytona Beach Community College to a 70–24 record from 2003 to 2006 and was twice named the Mid-Florida Conference Coach of the year. He served as assistant coach under Bob Huggins and Frank Martin at Kansas State from 2006 to 2012. In 2012, Martin left to become head coach at South Carolina, and Underwood followed him to Columbia as his associate head coach.
On April 30, 2013, Underwood was hired as head coach of Stephen F. Austin. He replaced Danny Kaspar, who left after 13 seasons to become the head coach of Texas State. According to athletic director Robert Hill, "Brad Underwood brings years of experience to SFA and has coached at the highest levels of Division I basketball. All of this plus his knowledge of the game and ability to recruit makes him the perfect hire for our men's basketball program. He has great plans on how we can make this program even better."

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