The Hokies (4-2, 1-1 Atlantic Coast Conference) scored two touchdowns in the opening 3½ minutes, forced three turnovers and had five sacks while avoiding their first 0-2 start to league play since joining the ACC a decade ago.
Elijah Hood had a short touchdown run and Marquise Williams rushed for 94 yards and was 17 of 33 for 187 yards passing.
He briefly made things interesting with his 9-yard touchdown pass to Quinshad Davis with 4:15 left.
The Tar Heels (2-3, 0-2) have lost their first two conference games for the second straight year.
This time, the offense - and not the maligned defense - was at fault. North Carolina - which allowed 70 and 50 points in its last two games - entered averaging a league-leading 40.8 points, while no power-conference team is allowing more yards (543) or points (44) per game.
The Tar Heels mostly bottled up Virginia Tech, holding the Hokies to a season-low 357 total yards. But Tech's defense neutralized North Carolina, which finished with a season-worst 323 yards.
And the Tar Heels' offense was responsible for the play of the game - by the Hokies.
Fuller jumped in front of redshirt freshman Mitch Trubisky's quick pass for Bug Howard and raced down the right side to make it 24-3 with 1:01 before halftime.
Neither offense did anything in the second half until North Carolina began clawing back into the game. M.J. Stewart intercepted Brewer at the Tech 16 with 13:32 remaining and Hood powered in from 1 yard out two plays later to make it 24-10.
Tech responded with a 15-play drive that chewed up 6:47 and ended with a 22-yard field goal by Joey Slye that made it a 17-point game with 6:28 left.
The Tar Heels countered by going 76 yards in six plays, capped by Williams' scoring pass, then forced a punt with about 3½ minutes left.
But return man Ryan Switzer fumbled the punt, Newsome recovered it at the UNC 10 and Coleman iced it by scoring from 1 yard out with 2:30 remaining.
This one looked like a runaway for the Hokies right from the opening snap - which was fumbled by Marquise Williams. Dadi Nicolas recovered for Virginia Tech at the UNC 16, and Marshawn Williams scored two plays later.
Hodges then split two defenders down the middle and Brewer hit him in stride for a touchdown pass that made it 14-3 on Tech's next series.
But that was it for a while - the Hokies' next 10 drives netted a total of 155 yards. Then came the long field goal drive and the special-teams turnover that put the game away.