Davis hit 7-of-9 attempts from the field and scored 18 points as part of North Carolina's third straight win.
The Tar Heels (11-3) have one game remaining, against College of Charleston Monday, before beginning Atlantic Coast Conference play Jan. 10 against Virginia Tech.
North Carolina grabbed a 23-8 lead and owned as much as a 37-point advantage in the second half before the Great Danes made a late run against members of the Tar Heels bench.
Deon Thompson added 15 for the Tar Heels, who shot 49 percent from the field and forced 23 Albany turnovers.
Albany (4-10) was led by Will Harris with 20 points.
Copyright 2009 by United Press International.
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