The Longhorns (20-13), who have never missed the NCAA tournament under Barnes, will be playing in the East Region. They are the No. 11 seed and will face Cincinnati (24-10) of the Big East on Friday in Nashville, Tenn.
Texas reached 20 wins for the 13th consecutive season by beating Iowa State, another NCAA team, in the Big 12 tournament. That likely solidified getting the Longhorns into the NCAA tournament before they lost to Missouri in the Big 12 semifinals.
The 14 straight NCAA tournament appearances for Texas is a school record and tied for the fourth most behind Kansas, Duke and Michigan State.
