Pepperdine (14-8, 7-4 West Coast) sent the Gaels to just their second loss in the conference (17-5, 9-2).
Murray's three-point play with 5:28 left put Pepperdine up 56-53. Brad Waldow tied it at 56 with three free throws but Murray's jumper with 2:09 left put the Waves back up 63-59.
Emmett Naar made 1 of 2 from the line to bring Saint Mary's within two with 48 seconds remaining, but Jeremy Major made a layup for Pepperdine, then Naar turned it over on the next possession and Pepperdine walked off with the upset.
Stacy Davis had 10 points and 12 boards for Pepperdine.
Saint Mary's led 33-28 at the break. Brad Waldow led the Gaels with 25 points and Naar finished with 14.