"People are going to start opening their eyes to us," said Houston designated hitter Jacob Lueneburg, who had three hits, including a bases-clearing double. "The 8-0 start is good, but that's behind us. Whatever happens in the rankings happens."
Houston's big seventh inning included Ashford Fulmer's two-run homer into the Crawford Boxes in left field that ended the scoring.
The Cougars, their 8-0 start their best since 1993, and Red Raiders opened the prestigious college tournament. The three-day event, which concludes on Sunday, also includes Rice, Texas, TCU and Sam Houston State.
"To win 9-0, that's a pretty good start," said Houston coach Todd Whitting. "It was well played for a long time. I was pleased with my ballclub's effort and the way they came out ready to play.
"We'll take wins against anybody. Texas Tech is a really good team. They have a chance of being a postseason team. I'm just happy to get a win in this tournament. It's important to get off to a good start."
The loss snapped Texas Tech's (8-2) eight-game winning streak. Red Raiders starter Dominic Moreno allowed only one run in five innings, but fell to 0-2.
Garza (3-0) allowed six hits and no walks with seven strikeouts. The right-hander threw 115 pitches. Tyler Ford came in to secure the last out for the Cougars' fifth shutout.
"You just want to go out there and give it everything you have," said Garza, who hit two batters in the first three innings. "You want to compete, whether it's 1-0 or 10-0. We want to go out there and get the guy out. That's our mindset. They hit a double, so what. Next pitch, we're going to get you out.
"It worked out great. We're ready to keep going."
Kyle Survance, Frankie Ratcliff and Casey Grayson each had two hits for the Cougars, who outhit the Red Raiders 10-6.