It was the fifth consecutive 20-point game for Clarkson, who was one of four Missouri (9-0) players in double figures.
Ernest Ross hit 5-of-11 shot from 3-point range in the victory. The Tigers, who trailed by eight points at halftime, made 10-of-26 shots from beyond the arc and shot 41.8 percent from the field.
The visiting Bruins (8-1) were led by Jordan Adams, who scored 22 points and had 10 rebounds. The loss ended a 14-game winning streak dating back to last season.
UCLA shot 37.7 percent from the field but made 5-of-20 3-point shots.