BYU (13-4, 3-0 West Coast) trailed 35-30 at halftime after shooting a dismal 9 for 32 from the field, but the Cougars were much better in the second half, hitting 58.1 percent of their shots.
Haws was 8 for 14 from the field including a perfect 7 for 7 from the free-throw line and Davies had nine rebounds to go along with his point total.
The Cougars started the second half with a 24-5 run and in the middle of it all was Matt Carlino whose 3-pointer with 14:14 remaining in the game gave BYU a 40-39 lead and the Cougars never trailed again.
Jordan Baker scored 20 points, grabbed five rebounds and had three assists to lead Pepperdine (9-7, 1-2).
College basketball fans should be excited about next season's Jimmy V Classic, an event that will feature Duke's heralded freshman class.
Jeff Goodman logs all the coaching changes following the 2015-16 college basketball season.
Can Josh Pastner keep top talent in Georgia? Will Tubby Smith change his recruiting philosophy at Memphis? New coaches face some difficult questions.