Jeffrey Moss added 12 points for Murray State (4-1).
Lamond Murray Jr. made a pair of free throws to give Pepperdine (2-3) a 55-53 lead with 1:43 to play.
Pepperdine's Stacy Davis missed a 3-pointer but Murray grabbed the offensive rebound. After a timeout, Davis was called for travelling and the Waves were forced to foul.
Moss hit two free throws with 11 seconds remaining to seal it.
Davis had 17 points and 11 rebounds and Murray scored 14 for Pepperdine.
Murray State scored 20 points off of 20 Waves turnovers.