The Tar Heels (15-2, 1-2 ACC), predicted by some to run the regular-season table, dropped its first two conference games before righting the ship on Thursday night behind Hansbrough's 67th game of at least 20 points -- the best in UNC history.
Ty Lawson scored 19 points with nine assists, while Wayne Ellington and Danny Green donated 13 points apiece for North Carolina, which shot just 42.2 percent from the floor but lived on the foul line (24-of-28, including 15- of-17 from Hansbrough).
Jamil Tucker led four Cavaliers (7-7, 1-2) in double figured with 12 points, Calvin Baker and Mike Scott added 11 and Mustapha Farrakhan donated 10. Virginia's super freshman and leading scorer Sylven Landesberg finished with only two points on 1-of-9 shooting.
The Tar Heels came out of the gates with enthusiasm, jumping to a 14-2 edge thanks in part to a Green three-pointer and a short jumper by Davis to close it out. Virginia eventually whittled the deficit to 15-14 on a pair of Baker free throws, but that is as close as it got for the remainder of the contest.
The lead grew to 44-31 late in the half on a two-handed Hansbrough slam, and the margin was 50-36 at intermission.
The second half was much of the same, as Lawson's three capped a 12-2 burst out of the break for a 62-38 advantage. Lawson's race-out lay-in moments later opened a 67-40 lead, and the rout was on from there.