Shadrach Thornton ran for 110 yards and a touchdown for the Wolfpack (6-5, 2-5 Atlantic Coast Conference), who became bowl eligible for the fourth time in five seasons.
N.C. State rushed for 362 yards, its highest total since 1990.
Wide receiver Bryan Underwood blew open the game when he scored on a 75-yard reverse on the first play from scrimmage of the second half.
The Wolfpack snapped a seven-game losing streak in home conference games, defeating Wake Forest (2-8, 0-6) at home for the 14th time in the last 15 tries.
John Wolford completed 15 of 32 passes for 161 yards for the Demon Deacons, who lost their 10th ACC game in a row and their sixth consecutive game overall.
N.C. State got a 2-yard touchdown run from Tony Creecy on its opening possession and never trailed.
The Wolfpack rolled despite a quiet performance by quarterback Jacoby Brissett, who was 8 of 19 for 83 yards.
Seven players carried the ball for N.C. State, and each of them averaged at least 6 yards per rush.
Dayes scored second-quarter touchdowns on a 1-yard run and a 7-yard reception to give the Wolfpack a 21-3 lead at halftime. He set up his first score with back-to-back big plays, turning a short pass into a 36-yard gain before exploiting a huge hole in the middle of Wake Forest's defense on a 30-yard run.
Wake Forest's season-long struggles on offense continued against an N.C. State defense that did not force a single punt against Georgia Tech the week before.
The Demon Deacons entered the game last in the Football Bowl Subdivision in total offense and rushing offense, and they were second to last in third-down conversion percentage.
Wake Forest went three and out on seven of its eight first-half possessions against the Wolfpack, totaling 87 yards on 35 plays.
The lone series in which the Demon Deacons picked up a first down was their third possession, when they put together a 15-play drive that resulted in a 32-yard field goal by Mike Weaver. Their other 20 snaps in the first half yielded a total of 25 yards.