The Cougars (8-2) were in such control that the game was stopped after seven innings because of the 10-run rule. Austin Pruitt (3-0) earned the vicory, striking out seven, and allowing five hits in a six-inning stint. In his previous start, Pruitt tossed a one-hit shutout.
"We kind of owed it to him as an offense," said Davis, who walked three times. "All the guys in front of me, they found a way on base and we just kept it rolling.
"We were patient at the plate. We had an approach and we knew what we were doing and we were able to execute."
Especially Cougars leadoff hitter Josh Vidales, who walked four times.
With 19 newcomers on this year's team, the Cougars are off to a fast start at the Classic. On Friday, Houston beat Texas A&M, 7-6.
"We had to learn to grow up fast," said Davis. "It's a sink or swim situation and we're swimming right now."
Caleb Barker's three-run double keyed the five-run second inning. Through two innings, the Cougars led 9-0. The Cougars needed only four hits in building an 11-2 lead in the fifth. Kyle Survance had two hits and three runs and Kyle Kirk had three RBIs and two runs for the Cougars, who play California on Sunday.
Baylor pitchers and fielders made it easier for the Cougars. Besides the 14 walks, seven Bears pitchers combined for one hit batsmen and one wild pitch. The Bears committed three errors and had three passed balls.
"Tonight, we took what they gave us," Houston coach Todd Whitting said. "We sat in the box and didn't try to force it. Swung at our pitch and took our walks. Even though we went up by nine early, we still had good at-bats all the way through."
Nathan Orf scored two runs for Baylor (4-6) and Cal Towey had two RBIs. Bears starter Austin Stone (0-1) took the loss.
Richard Dean is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.