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).
Seton Hall sophomore Isaiah Whitehead will stay in the NBA draft and not return for his junior season.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.
Gonzaga center Przemek Karnowski, who missed most of last season with a back injury, says he is returning for another year.