The Bulldogs broke open what had been a tie game midway through the first half to take a 39-21 advantage at the break.
Dower made all seven of his field goal attempts while Kevin Pangos had 14 points and Przemec Karnowski had 11.
Gonzaga (15-3, 5-1 West Coast Conference) limited Pepperdine to 32 percent shooting.
The Waves (11-8, 4-3 WCC) were led by Stacy Davis with 12 points, the only Pepperdine player in double figures.
2014: The Year in Music [PHOTOS]