Danielle Butts added 10 points and eight rebounds for the Tar Heels (9-1), who have won two straight since a lopsided loss at Tennessee.
North Carolina won despite shooting 27 percent (17 of 62) for the game. But the Eagles (0-11) were even worse against a team ranked 23rd nationally in field-goal percentage defense.
N.C. Central missed 17 of 19 shots in the first half and trailed 21-6 at the break. The Eagles made just five shots after halftime and finished at 16 percent (7 of 43) for the game.
Tisha Dixon had eight points and 12 rebounds to lead NCCU, while Chasidy Williams scored seven.
The Tar Heels have won all six meetings with Central by an average margin of more than 45 points.
Wednesday's outcome matched a pair of UNC records as NCCU's 21 points tied Savannah State in 2011 for the fewest points ever scored against Carolina. The 49 points for the Tar Heels tied a record for fewest points in a win that was set against Virginia in 1976 (49-40) and matched vs. Villanova in 2002 (49-45).
Carolina will make its annual trip to the Myrtle Beach, S.C., area for a pair of games before a nine-day break. The Tar Heels will face Coastal Carolina in Conway, S.C., Sunday afternoon at 2 before taking on East Carolina at the Myrtle Beach Convention Center Wednesday night at 7.