The Buffaloes made only 20 field goals, went 5-of-17 from 3-point range and committed 17 turnovers.
Powell converted 8-of-13 shots, two of them from long range, and was backed up by 14 points and 13 rebounds from Jordan Adams.
UCLA (14-3, 3-1 Pacific-12 Conference) claimed 14 offensive boards, twice as many as Colorado.
The Buffaloes (14-4, 3-2 Pac-12) were led by Askia Booker with 21 points.
Colorado played its first game without Spencer Dinwiddie, the team's leading scorer who was lost for the season last Sunday when he suffered a torn knee ligament in a setback at Washington.