Baylor held the Longhorns to 20 points and 26 percent shooting in the second half.
Forward Jo Lual-Acuil Jr. and guard Manu Lecomte each scored 17 to lead Baylor (11-4, 1-2 Big 12). Bears forward Mark Vital added 10 points and a team-high seven rebounds.
Guard Jase Febres finished with 18 to lead Texas (10-5, 1-2). Forward Mohamed Bamba scored 15 with nine rebounds.
Texas coach Shaka Smart dipped to 0-5 against Baylor.
Baylor led by nine when Jake Lindsey hit a pair of free throws midway through the second half.
Texas fought back with a 9-2 run and cut Baylor's lead to 57-55 when forward Dylan Osetkowski made a deep 3-pointer from beyond the arc at the top of the key.
But Baylor pulled away at the end, finishing the game on a 6-0 run in the final 2:07.
Febres scored all 18 of his points in the first half, leading the way as Texas surged ahead by as many as seven.
The Longhorns took a 19-13 advantage when Eric Davis Jr. made a pair of free throws with 11:16 left before the break.
But Baylor responded with a 14-6 run, sparked by Lindsey hitting a 3-pointer and making a layup in transition. Lecomte capped the spurt with a jumper for a 27-25 lead with 6:58 left in the first half.
Texas pulled ahead again using a layup by Febres, a dunk by guard Kerwin Roach II and a Febres 3-pointer for a 40-33 margin with just 1:29 left before the break.
But again the Bears fired back, with Lindsey making a layup and Lecomte nailing a 3 just before the first-half buzzer to cut the Horns' lead to two at halftime.
After back-to-back home games, Baylor goes on the road next week for matchups at West Virginia and Iowa State.
Texas returns home to host No. 16 TCU on Wednesday.
--Field Level Media
Texas | Baylor | |
Jase Febres 18 | Scoring | Manu Lecomte 17 |
Matt Coleman 5 | Assists | Manu Lecomte 4 |
Mohamed Bamba 9 | Rebounds | Mark Vital 7 |
Eric Davis Jr. 4 | Free Throws Made | Manu Lecomte 5 |
Mohamed Bamba 2 | Steals | Jo Lual-Acuil Jr. 3 |
Mohamed Bamba 5 | Blocks | Jo Lual-Acuil Jr. 4 |