Texas starter Adrian Alaniz allowed just one run in seven innings, shortstop Seth Johnston homered and the Texas Longhorns quieted Big 12 and state rival Baylor, 5-1, in the opening round of the College World Series on Saturday. Texas (52-16) advanced to face Tulane, which beat Oregon State. Baylor (44-23) will play the Beavers in an elimination game. The Longhorns were 0-4 against Baylor this year before Saturday's victory. Alaniz gave up just seven hits -- all singles -- and Texas got out to an early 2-0 lead on a two-run home run by Johnston. Baylor put up a run in the fourth with a two-out, RBI base hit by shortstop Paul Witt. But Texas tacked on two more runs in the sixth and another in the eighth. In the earlier game, Scott Madden's pinch-hit, two-run double in the seventh inning was the difference as top-seeded Tulane escaped with a 3-1 win over eighth seed Oregon State.