Howell's layup off a Scott Woods assist with 1:56 remaining broke a 57-57 tie and his subsequent foul shot gave the Wolfpack (15-3, 4-1 ACC) the momentum they needed for the win, which kept them unbeaten at home.
Howell finished with 11 points and 12 rebounds. Rodney Purvis and Wood each added 11 points as N.C. State bounced back from a Wednesday loss to Maryland.
Devin Booker went 13-of-18 from the field en route to 27 points, but it wasn't enough for Clemson (10-7, 2-3).
Rod Hall also reached double figures for N.C. State with 16 points.