Freshman Joel James added 13 points and seven rebounds for the Tar Heels, who missed 10 of their first 11 3-point attempts and trailed early in the second half before ripping off 23 consecutive points.
Karron Johnson had 17 points for the Bears, a member of the Division II Central Intercollegiate Athletic Association.
UNC's starting wing players shot a combined 6 for 19, but reserve Leslie McDonald had 12 points. P.J. Hairston scored eight straight points - including a pair of 3-pointers - to spark the team's second-half surge.
The Tar Heels open the regular season Nov. 9 against Gardner-Webb.