Cincinnati wasted all of a 19-point lead, but Yancy Gates made sure the Bearcats didn't completely fold.
Gates scored four of his 15 points during a critical six-point burst in the final minutes, helping Cincinnati to a 65-59 victory over Texas in the second round of the NCAA Tournament.
Jaquon Parker helped the Big East Tournament runners-up build an early 16-2 advantage and finished with 13 points for the Bearcats (25-10), who are seeded sixth in the East Region and will next face the winner between Florida State and St. Bonaventure in Sunday's third round.
J'Covan Brown scored 19 points and Julien Lewis added 14 for Texas (20-14), which was making its 14th straight NCAA Tournament appearance. The Longhorns have lost their opening tournament game twice in the past three years.