"It's a historic day for TCU," coach Jim Schlossnagle said. "Going to Omaha is incredibly hard, and doing it here, against a great, great program and the greatest coach in the history of the sport is an honor."
The Horned Frogs (51-12) scored the first run of the game in the bottom of the fifth when Jason Coats hit an RBI single off Brandon Workman (12-2) down the first-base line to score Taylor Featherson who hit a leadoff double and advanced to third on a throwing error.
Texas closer Chance Ruffin gave up the last three runs on two homers. Schultz sent Ruffin's 2-2 pitch over the left-field fence to put TCU up 3-0 in the seventh inning.
"I was just looking for him to make a mistake with his slider, which is a really good pitch, and he did," Schultz said. "I just put a good swing on it."
Ruffin, who entered the game having only given up five earned runs and two homers in 36 appearances, gave up another home run in the eighth to Bryan Holaday that put TCU up 4-0.
"It's like a bad dream," Ruffin said. "You really wish you could have it back and do it all over again. It's just an indescribably bad feeling."
Kyle Winkler (12-2) gave up no runs and five hits with five strikeouts in 7 2-3 innings for the Horned Frogs despite struggling early on.
In the first inning, with men on second and first, Winkler struck out Cameron Rupp looking. And in the second, with a man on second with one out, Winkler was able to force back-to-back fly outs to get out of the inning.
"It's not the situation you want to be in at all," Winkler said. "I just got lucky. We made some good defensive plays in the outfield. I was just able to pitch out of it and make my pitches."
Texas (50-13) avoided the shutout in the ninth when pinch-hitter Paul Montalbano scored from second on an error by Jerome Pena.