John Henson added 20 points and 12 boards for the Tar Heels (2-0), who began their season Friday with a defeat of Michigan State at the Carrier Classic in San Diego.
Harrison Barnes netted 17 points in the victory, during which UNC made 59 percent of its shots. Barnes, Zeller and Henson combined to make 22-of-34 shots.
By contrast, UNC-Asheville made 25-of-63 shots as a team. J.P. Primm scored 23 points and Jaron Lane had 21 for the Bulldogs (0-2), who lost at NC State on Friday to open their season.