Stacy Davis and Jorne Jackson also had 11 points while Jordan Baker chipped in 10. Raines, a freshman, made all four of his shots from the field and all three free throw attempts.
Alabama State (1-10) took its first lead of the game, 12-11, following a Joshua Freelove 3-pointer. But Pepperdine retook the lead behind an 11-4 run. Raines capped the spurt with a three-point play as Pepperdine (7-4) led 23-15 and took a 30-21 advantage into halftime.
The Hornets cut the deficit to 50-44 with 5:13 left to play, but Baker made a free throw and a 3-pointer and Davis hit a jumper to help Pepperdine pull away.
Pepperdine shot a season-high 53.8 percent (21 of 39).
Freelove led Alabama State with 14 points.