Aaron Gordon had a double-double of 10 points and 12 rebounds for the Wildcats (20-0, 7-0 Pac-12), who couldn't shake off the Utes until late in the second half en route to school-record 20th consecutive win.
Arizona's victory was also its 17th straight at home.
The Utes (14-6, 3-5) were led by Delon Wright with 19 points and six rebounds.
Jordan Loveridge also reached double figures with 13 points.
Celebrity Families of 2014 [PHOTOS]