Nesbitt scored twice after 32 carries for 97 yards and also completed 7-of-11 passes for 89 yards.
Running back Jonathan Dwyer, the 2008 ACC Player of the Year, helped Tech maintain ball control by gaining 158 yards on 19 carries.
Roddy Jones rushed for a touchdown, while receivers Stephen Hill and Demaryius Thomas combined to make five receptions for 73 yards for the Yellow Jackets (3-1, 2-1 ACC), whose defense held the Tar Heels to just 17 rushing yards and 154 overall.
UNC quarterback T.J. Yates was 11-for-26 for 137 yards, one touchdown and two costly interceptions.
He entered the contest with a 67.1 percent completion average.
Erik Highsmith caught six passes for 107 yards and the touchdown for the Tar Heels (3-1, 2-1 ACC).