The Bruins (2-1) were up by only five points midway through the second half when they went on a 16-4 run to pull away from the Waves.
The Bruins were playing their second consecutive game without suspended forward Nikola Dragovic, their only returning starter. Gordon added nine rebounds and Roll, who hit five 3-pointers, had five assists. Guard Malcolm Lee added 13 points for the Bruins.
Pepperdine (1-3) was led by guard Keion Bell's 22 points, but no other Wave reached double figures in scoring.
Bell has scored at least 20 points in each of Pepperdine's four games. He reached the 20 mark only three times last season despite being the Waves' leading scorer
UCLA trailed 6-4 early, but never again. The Bruins offense started slowly, but they shot 54.3 percent by the night's end and ran away with the game in the closing minutes. UCLA was also 13 of 15 from the free-throw line.
Dragovic was on the UCLA bench in street clothes. He was suspended for a second game following his arrest for assault last Friday.
UCLA also played without starting guard Jerime Anderson for most of the second half, losing him to leg cramps. Mustafa Abdul-Hamid came off the bench in his place and added a career-high 10 points for the Bruins.