Callahan scored 20 and Davis 19, with Davis connecting on 13 of 15 from the foul line and also pulling down seven rebounds. Ricky Tarrant added 13 points and six assists for the Green Wave (9-3).
Tulane opened on a 9-2 run that included five points from Callahan, but the Waves charged back to take a 12-11 lead after back-to-back jumpers by Stacy Davis. The Green Wave responded with a 7-0 run, capped by Callahan's 3, and Tulane led the rest of the way.
The Green Wave led 30-24 at the half and 44-41 with 11:04 left, but then Josh Davis' three-point play sparked a 17-4 run to put the game out of Pepperdine's reach.