The Tar Heels (2-3, 2-1 Atlantic Coast Conference) held the ball for most of the day as the Wolfpack (2-1, 0-1) failed to generate much offense against the nation's 19th-ranked defense until the final five minutes.
North Carolina beat Florida State 41-9 last week for its first win of the season.
The point total by N.C. State was lowest in 15 games under coach Chuck Amato. The Wolfpack had scored 30 or more points in 10 of 14 prior to Saturday behind quarterback Philip Rivers.
But Rivers couldn't get the ball deep through three quarters and N.C. State's running game wasn't as clutch as last year when the Wolfpack won 38-20 in Chapel Hill.
Rivers threw for 306 yards, but didn't get the Wolfpack into the end zone when it counted. N.C. State turned it over on downs after driving to the North Carolina 31 and 26 on its last two series.
Jeff Reed's 36-yard field goal with 6:20 left in the third quarter gave the Tar Heels a 10-6 lead. Durant then drove North Carolina 83 yards, capping the six-minute march with a 19-yard scoring pass to a wide open Bailey.
Durant found Bailey in the same vicinity early in the first quarter as North Carolina took a lead it never surrendered on its way to beating the Wolfpack for the eighth time in the last nine meetings.
The Wolfpack managed just eight plays in the third quarter with a strong wind as the Tar Heels took control.
N.C. State trailed 7-6, but elected to go for it on fourth-and-2 at the North Carolina 22 on its first series of the third quarter because of an ankle injury to place-kicker Austin Herbert.
The pass by Rivers sailed over the head of Willie Wright and the air seemed to go out of the Wolfpack.
N.C. State only trailed by one at the half after a miserable start.
The Wolfpack fumbled twice and had 46 yards in penalties in the opening 15 minutes as it appeared the Tar Heels would take control.
A fumble by wide receiver Sterling Hicks at the N.C. State 27 set up North Carolina's first score less than eight minutes in.
The short scoring drive was also aided by a personal foul penalty as Durant found Bailey in the front corner of the end zone from 14 yards out.
N.C. State fumbled twice more in the second quarter, but the Tar Heels failed to take advantage of their excellent field position.
North Carolina drove to the Wolfpack 33, 32 and 15 and didn't score.
Ronald Curry and Durant were each intercepted, and Reed missed a 32-yard field goal attempt. It was Reed's first miss from inside the 40 in 16 career attempts.
Rivers drove the Wolfpack 71 yards for its only score of the half, capping the march with a 23-yard TD pass over the middle to Dovonte Edwards, who caught the ball and then slammed into the base of the goal post.
Backup Adam Kiker missed the extra point. Herbert sprained his right ankle late in the week walking down some steps and just handled the punting.
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