Khleem Perkins scored 17 points for the Coyotes.
The Bruins were without senior center Travis Wear, who was diagnosed with appendicitis this week.
UCLA led by 13 points in the first half, but the Coyotes whittled that lead to three points by halftime.
The Bruins used a 12-2 run in the opening minutes of the second half to make it 54-41. They had a 53-35 rebounding advantage.
