The Longhorns' third win in a row is an important one for a team desperate to build its NCAA tournament resume over the final weeks of the regular season.
Texas trailed 40-27 at halftime before battling back. Brown, the Big 12's leading scorer, made a deep 3-pointer to put the Longhorns ahead with just over 8 minutes to play.
Wangmene had his first career double-double for Texas (16-9, 6-6 Big 12). His 15 points and 13 rebounds were both career highs.
Angel Rodriguez scored 15 points for Kansas State (17-7, 6-6), but the point guard also had six of his team's 16 turnovers.