Pepperdine (15-8, 8-4 West Coast Conference) had a 6-0 run to take its first lead in over 20 minutes at 62-61 with 7:42 left.
BYU (17-8, 7-5) took the lead back briefly, but the Waves went in front for good on Jeremy Major's 3-pointer with 5:28 left which, at 65-64, started a 12-1 run over the next 3 ½ minutes.
Davis had 17 second-half points, Murray 14 and Jett Raines scored all of his 14 after the break. The Waves trailed by 16 late in the first half.
BYU had a 14-0 run in the first half to lead 27-14. Tyler Haws scored 22 to join Jimmer Fredette as the only Cougars to reach 2,500 career points. It was also Haws' 68th career 20-point game, a BYU record.