Texas defeated TCU in the other opening-round game 70-57.
Wednesday's two winners will meet the conference co-champions in Thursday's quarterfinals -- Texas Tech taking on No. 6 Kansas and Texas facing 12th-ranked Kansas State. The other quarterfinals will send Oklahoma against Iowa State and Oklahoma State against Baylor.
Jaye Crockett scored 18 points to lead Texas Tech (11-19), which quickly ended the Mountaineers first appearance in the Big 12 Tournament.
Julien Lewis made four 3-pointers and scored 19 points for Texas (16-16) in its victory over the Horned Frogs. The Longhorns pulled away in the second half after owning only a two-point lead at the break.
TCU's season came to an end at 11-21, but the Frogs had the consolation of pulling off one of the year's biggest upsets in college basketball -- a victory over Kansas.