Haws shot just 4 of 12 from the floor but made all 14 free-throw attempts for the Cougars (21-10, 10-6 West Coast), who never trailed after 8:18 remained in the first half.
Haws' last two free throws made the score 73-67, and Anthony Ireland hit a 3-pointer with two seconds remaining for the Lions (8-22, 1-15). Ireland scored 24 points and Ashley Hamilton 18 for Loyola Marymount.
While the game was in progress, BYU clinched the No. 3 seed in the WCC tournament in Las Vegas when Santa Clara lost at Saint Mary's. Santa Clara is the No. 4 seed; both schools earn a bye to the quarterfinals.
Loyola Marymount entered the game already locked into the No. 9 seed and faces No. 8 Portland on Wednesday.
ESPN's Dan Dakich joins The Paul Finebaum Show to discuss the SEC's presence in the NBA Draft.
Ted Kapita was the top-rated recruit from West Virginia in the class of 2015 and recently played at DME Academy in Florida.
With the Suns drafting Tyler Ulis, they now have five guards on their roster who attended Kentucky.