True freshman Kasparek set up the Horns for victory, pitching six-plus innings and surrendering just one run on seven hits while striking out three and walking two.
The Cowboys got on the board first with a single run in the second but Texas broke through for 4 runs in the top of the fifth. Nick Peoples led off the top half of the inning with a bunt single and David Maroul's sac bunt moved Peoples into scoring position. Thomas Incaviglia followed with a single to left that scored Peoples and squared the game at 1-1. But Robby Hudson followed with a single to left and Drew Stubbs walked to load the bases, setting the plate for Longhorn leading hitter Seth Johnston. The senior shortstop singled to right to drive in Incaviglia and Hudson and give the Horns the lead for good. In the inning, Chance Wheeless added to the advantage with a safety squeeze to score Stubbs.
Texas padded its lead with two more in the top of the seventh, but with Kasparek (6-0) and then closer J. Brent Cox on the hill, the Horns had all they would need to advance.
Saturday morning, Cory VanAllen is expected to take the hill for Baylor and Kyle McCulloch, UT's ace who has remained in Austin to receive treatment for a sore back, is traveling Friday night to Oklahoma City and is expected to start for the Horns.