Texas (18-12) improved to 7-10 in the Big 12 with one game remaining, keeping its hopes for an NCAA tournament bid alive. Last season, Oklahoma State became the first Big 12 team to get an at-large bid with a losing conference record (8-10).
Baylor (22-8, 10-7) had a chance to tie, but Kenny Chery's shot was blocked by Myles Turner with 1 second left.
Seven players from both teams were ejected in the overtime for leaving the bench during a brief skirmish between Taylor and Baylor's Royce O'Neal.
Demarcus Holland led Texas with 12 points. Kendal Yancy scored 11, one more than Javan Felix, who began the overtime with a 3-pointer.
Taurean Prince led Baylor with 17 points. Rico Gathers had 12 points and 11 rebounds.
After an exchange of turnovers in the overtime, Taylor and O'Neal fell to the court, prompting the brief skirmish. Four Longhorns, including starters Yancy and Cam Ridley, were ejected along with key reserves Prince Ibeh and Connor Lammert. Three Baylor players, starter Johnathan Motley and subs Ishmail Wanright and John Heard, were tossed.
Texas' Jon Holmes hit a long 3-pointer with 1:04 left to tie the game at 54. Ibeh blocked a driving shot by Chery, giving the Longhorns a chance to win. After calling a timeout, the Longhorns could not find a good shot, and regulation ended with a forced 3-point attempt by HolmesBaylor took a nine-point lead 29 seconds into the second half on a jump shot by Chery. The Bears then went 7:40 without a field goal, settling for two free throws and allowing Texas to creep closer. The Bears missed 12 straight shots, some because of stout Texas defense around the rim, before Prince made a layup.
During that drought, Texas cut the deficit to one on a 3-pointer by Felix with 14 minutes remaining.
But Baylor, which had difficulty scoring inside against the taller Longhorns, relied on 3-point shooting to regain a measure of control. Prince, Lester Medford and Al Freeman all made one during a span of less than 3 minutes, stretching the lead to 10. Freeman's 3 with 7:40 left barely beat the 35-second shot clock on a strong defensive possession by Texas.
The Longhorns made one more push, closing within three with 3 minutes remaining, but Prince responded with another 3-pointer.
Texas: The Longhorns, who have five players between 6-foot-8 and 6-11, lead the nation in blocked shots with nearly eight a game. They set a school record with 14 during a loss at Kansas on Saturday. But they have not used their length and athleticism to induce turnovers by opponents. They rank last in the Big 12 with nine a game. Coach Rick Barnes says his guards are not aggressive enough in that area.
Baylor: The Bears have been fast starters this season, getting outscored in the first half only three times. In those games, they beat Memphis in Las Vegas but lost at Oklahoma and Oklahoma State. Baylor has outscored opponents in the first half in its last 10 games.
Texas hosts Kansas State on Saturday.
Baylor hosts Texas Tech on Friday.