Houston (24-9) advances to face Tulsa (22-13) in the semifinals Wednesday.
Urule Igbavboa led Valparaiso with 16 points. Jarryd Loyd added 15 for the Crusaders (22-14).
Houston led by 13 at the half and gradually pulled away in the second half. An 11-2 run helped by a pair of 3-pointers by Lewis gave the Cougars a 70-47 lead with 10:18 remaining in the game.
The lead changed hands six times and it was tied four other times in the first 15 minutes of the game.
Then McKiver scored six points in a 10-2 Houston run as the Cougars took a 39-29 lead with 3:12 to go in the first half.
A 3-pointer by Marcus Malone with 38 seconds left gave Houston a 45-32 lead at the half.