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).
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Five-star guard Coby White only needed three days to accept an offer from head coach Roy Williams. White, No. 21 in the ESPN 60 committed to the North Carolina Thursday.