Texas ended a season of injuries, player suspensions and head-scratching losses with its best game of the year.
James Brown passed for a school-record five touchdowns, two to Eric Jackson, as the Longhorns used big plays to defeat Baylor, 63-35, on Thursday at Waco, Tex.
"This is the kind of win that shows we deserve to go to a bowl game," linebacker Norman Watkins said. "It shows how strong we are, to go through all of the controversies this season and finish the year with our best game."
Texas (7-4, 4-3 Southwest Conference) will play in the Sun Bowl in El Paso on Dec. 30.
Baylor (7-4, 4-3) had Cotton Bowl hopes heading into the game, but is likely headed to the Alamo Bowl in San Antonio on Dec. 31. The Longhorn victory also means that Texas Tech will be the Southwest Conference representative in the Cotton Bowl.
Brown, a redshirt freshman, completed 18 of 25 passes for 289 yards without an interception and also ran seven times for 51 yards.
Texas' offensive output was its best under third-year Coach John Mackovic, who resumed calling the plays after loses to Rice, Texas Tech and Texas A&M; had fans calling for his job.
The resurgent Mountaineers (7-5, 4-3), playing at home, won for the sixth time in seven games to remain in contention for the Carquest and Independence bowls.