Parker French (4-3) scattered eight hits and struck out six in a complete game for the fourth-seeded Longhorns (27-25).
Fifth-seeded Texas Tech (30-23) scored after three consecutive singles and a passed ball in the seventh inning. But with runners on first and second, French got a fly out and a strikeout to end the inning.
Red Raiders starter Cameron Smith (6-5) allowed five hits and one earned run in 6.1 innings and struck out a career-high eight. Texas Tech stranded seven base runners, including two in the ninth inning.
Texas advances to play the winner of No. 1 TCU vs. No. 8 Baylor on Thursday. Texas Tech will face the loser of TCU vs. Baylor in an elimination game.