Watson threw for 383 yards and five scores, and also ran for 54 yards and a touchdown for the Tigers (8-0, 5-0 Atlantic Coast Conference), who are closing in on an appearance in the ACC championship game and chasing a College Football Playoff berth.
The Tigers host No. 17 Florida State next week with a chance to wrap up the ACC's Atlantic Division title.
Wayne Gallman ran for 172 yards and a touchdown for Clemson, who put together a lightning-strike scoring drive right before halftime to go ahead for good.
The Tigers led by 20 after halftime and finished with 623 total yards, spending the final quarter answering desperate scoring drives from the Wolfpack (5-3, 1-3) to remain in firm control.
It wasn't perfect for Clemson, with N.C. State breaking off a few big plays and turning the game into a shootout while playing from behind. But the Tigers were never seriously threatened in the final 20 minutes, leading by at least 12 on their way to an 11th straight victory dating to last season.
It also marked Clemson's 36th straight win against teams unranked in the AP Top 25, the last loss coming at the Wolfpack in 2011.
Jacoby Brissett threw for three touchdowns and ran for one, while Jaylen Samuels also ran for a score for the Wolfpack. Freshman Nyheim Hines had a 100-yard kickoff return for a touchdown in a wild opening 5 minutes that saw both teams score twice and even block a PAT.
But N.C. State played the second half without top rusher Matt Dayes due to what was described as lower-body injury. And the Wolfpack never found a way to slow Watson and the Tigers consistently.
N.C. State led 20-19 before it got away, with freshman Kyle Bambard missing a 44-yard field goal with 55 seconds left in the half. The Tigers pounced, with Watson finding Artavis Scott for a 31-yard pass then going deep to Charone Peake for a 42-yard touchdown to cap a two-play, 15-second drive that put Clemson on top to stay and sucked some of the energy from a hostile crowd.
By the time Watson found Zac Brooks for a 35-yard TD late in the third, Clemson's lead had grown to 47-27.
And by the end, N.C. State had lost by the same score as the last time it hosted a top-five opponent: top-ranked Florida State and reigning Heisman Trophy winner Jameis Winston last season.