The Tar Heels held the Hokies scoreless for nearly 7 minutes and outrebounded them 49-22, allowing them just four on the offensive glass.
Adam Smith had 11 points to lead Virginia Tech (8-9, 0-4), which cut an 18-point deficit to eight and closed to 61-53 on Smith's 3-pointer with just over 2 minutes left.
Theo Pinson countered with a dunk, and J.P. Tokoto, Brice Johnson and Nate Britt combined to hit 5 of 6 free throws in the final minute.
Shane Henry added 10 points for the Hokies, who made more 3-pointers (10) than 2-pointers (nine) but shot just 36 percent. They lost their fifth straight overall and fell to 0-5 on the road.
Tokoto finished with 10 points for the Tar Heels, who never trailed but struggled to give themselves much separation in a largely disjointed game.
The difference came during the 7-minute stretch of the first half in which North Carolina first pushed its lead into double figures late while Virginia Tech - a 47 percent shooting team - lost its touch from the field.
North Carolina scored 11 straight points during a 15-3 run that ended on Kennedy Meeks' layup that made it 34-19 with under 2 minutes before the break.
During that time, the Hokies simply went cold: After Jalen Hudson's 3 pulled them to 19-16 with just under 10 minutes to go, they missed 10 straight shots.
Virginia Tech: The Hokies fell to 6-45 in conference games in the series with North Carolina, which includes both the ACC and Southern Conference.
North Carolina: The Tar Heels didn't attempt a free throw in the first half - its first half without a foul shot in two years.
North Carolina is at Wake Forest on Wednesday night.