The Bruins had only a three-point lead with 12:30 to play, but that advantage grew to 14 points with less than four minutes remaining.
UCLA won its fourth game in as many starts while the Eagles slipped to 4-2.
Adams made 10-of-18 from the field and all eight of his free throw attempts. He also grabbed seven rebounds. Anderson had 13 points, 12 rebounds and 11 assists.
Chad Posthumus scored 21 points for Morehead State and dominated the boards with 18 rebounds.