The Utes (19-7, 8-5 Pac-12 Conference) remain in striking distance for the conference's regular-season title.
Utah went on a 17-3 run that included 14 points from Poeltl to take a 21-9 lead. A 17-5 stretch, highlighted by two three-point baskets by Jordan Loveridge, pushed the lead to 40-21 after the first half.
The Cougars (9-16, 1-12) never found an answer for Poeltl. The 7-footer scored seven points during a 13-0 run that gave Utah a 55-24 lead.
Poeltl made 11 of 14 shots from the field and finished with 10 rebounds. Loveridge had 14 points and Brekkott Chapman scored a season-high 12 points.
Que Johnson scored 13 points for the Cougars, who shot a season-low 30.6% from the field.