The Demon Deacons (7-1, 3-1 Atlantic Coast Conference) have won seven of eight to start the season for the first time since 1979 and third time in school history. They swept Tobacco Road rivals North Carolina, N.C. State and Duke for the first time since 1987.
Wake Forest trailed 17-14 before Sam Swank tied it with a 41-yard field goal on the second play of the fourth quarter.
Then, almost immediately, the Demon Deacons' defense helped its offense take the lead for good.
North Carolina was trying to get something going when Cam Sexton found fullback Nick Starcevic toward the right sideline. But Demon Deacons linebacker Stanley Arnoux stripped Starcevic and Josh Gattis recovered at the Tar Heels' 39.
On the next play, Skinner found Moore over the middle for the go-ahead touchdown.
North Carolina had one last chance to force overtime, converting two fourth downs on its final drive and advancing to the 3 on Dailey's 44-yard sideline pass to Hakeem Nicks. But three plays later, Abbate stepped in front of Dailey's final pass.
Moore, who also rushed 34 yards on a reverse for a TD, finished with six receptions for 82 yards to lead the Demon Deacons, who remain in contention in the ACC's jumbled Atlantic Division.
North Carolina (1-7, 0-5) was playing its first game since the firing of coach John Bunting, effective at the end of the season, and the Tar Heels fell to 0-7 against I-A opponents.
Ronnie McGill had 100 of his 117 yards rushing in the first half and became just the second running back this season to rush for at least 100 yards against the Demon Deacons, joining Clemson's C.J. Spiller. McGill also had a 1-yard touchdown run.
Dailey, making his first start since Week 2 and alternating every other series with Sexton, finished 13-of-19 for 156 yards with one touchdown and two interceptions.
Skinner was 7-of-8 for 89 yards for Wake Forest, which never trailed during the first half but fought off several North Carolina comeback attempts.
Wake Forest took an early 7-0 lead after returning a blocked punt for a TD. Alphonso Smith burst through the middle, smothered David Wooldridge's punt and returned the ball 16 yards for the first score.
North Carolina tied it on its following possession on Dailey's 1-yard touchdown pass to converted tackle Andre Barbour.
Connor Barth kicked a 35-yard field goal in the third quarter to give North Carolina its first lead in a span of nearly 10 quarters, dating back to the first quarter against South Florida on Oct. 14.