Heading into the break, the Wildcats held a 7-3 shot advantage over the Eagles.
Going downwind in the second half, the Wildcats managed to outshoot the Eagles 18-5. Odaine Sinclair put the game out of reach in the 76th minute after he received a ball in the box off a throw-in from Sean McAlister.
Baker goalkeeper Matt Bickley made one save in the contest to record his eighth shutout of the season.
“It was a really exciting night,” Houser added. “Now the guys get to put their talent up against some of the best in the country next week in Alabama.
The Wildcats will return to action on Nov. 28 when they face Huston-Tillotson (Texas) in the round of 16.
View the box score here.