Frazier went 12-of-14 from the free-throw line and Fahro Alihodzic grabbed 13 rebounds to go with eight points for the Blazers (6-2), who won despite shooting an anemic 30.6 percent from the field.
The Tar Heels (4-2) also had trouble shooting, missing 11-of-12 three-point attempts in their second loss to a non-conference foe in four games.
Marcus Paige (13 points) attempted to produce a tie with 9 seconds left but his 3-point shot was blocked by UAB's Robert Williams.
J.P. Tokoto scored 16 points for North Carolina.
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