Howard also caught a backbreaking 17-yard touchdown pass from change-of-pace quarterback Marquise Williams late in the third quarter. Williams and A.J. Blue had short scoring runs for the Tar Heels.
Andre Williams, the ACC's leading rusher, ran for 172 yards in his fifth 100-yard performance of the season and had a 56-yard touchdown run.
But facing a defense that allows an ACC-worst 456 yards per game, the Eagles (3-4, 1-3) managed just 261 total yards and converted just 5 of 16 third downs. Until the final five meaningless minutes, they took only five snaps in North Carolina territory.
Chase Rettig was 10 of 20 for 57 yards and was sacked four times for BC.
The Eagles lost their sixth straight ACC road game, have yet to beat North Carolina since joining the ACC in 2005 and have never won in Chapel Hill.
For the Tar Heels, it only felt like that long since their last win here - or anywhere, for that matter.
A rough stretch - including consecutive games against nationally ranked Coastal Division rivals Miami and Virginia Tech - left them with the worst record in the ACC.
But this game started a stretch of navigable games: The second half of the schedule includes a game against FCS member Old Dominion and five league opponents who entered the weekend a combined 17-15.
North Carolina's maligned defense, which entered last in the league in all four major stat categories, kept the Eagles in check for much of this one.
The only real mistake came on the BC tailback's long touchdown run, in which Williams was barely touched on his way up the middle and down the right side.
Blue put the Tar Heels back up on the fifth play of the second when he burrowed in off left tackle. Renner then extended North Carolina's lead to 20-7 with his scoring pass to Howard with 52 seconds left in the half.
Howard's second score came with 19 seconds left in the third and after the Tar Heels moved into the red zone on two Renner-to-Eric Ebron completions. Cornerback Bryce Jones slipped near the back line, leaving Howard wide open for the easy strike from UNC's Williams to stretch the lead to 27-7.
Marquise Williams' 4-yard TD run midway through the fourth then pushed it to 34-7.
Switzer, a freshman who had two touchdowns called back due to penalties earlier this season, finally got his first scoring catch on North Carolina's first drive to put the Tar Heels up 6-0. That came after Williams fumbled at the BC 35 on the Eagles' second offensive play.
Nate Freese kicked a 38-yard field goal with 2:04 left for BC.