The 15th-ranked Wolfpack held a three-point lead at the break, but the Bulldogs moved in front and maintained a narrow advantage throughout most of the second half.
North Carolina State finally took the lead for good on a layup by Howell with 3:06 to play and his clutch free throws wrapped up the victory.
Sam Hughes scored on a layup for the Bulldogs just before the buzzer to account for the final score.
Howell led the Wolfpack with 23 points and also grabbed 15 rebounds. Lorenzo Brown added 19 points.
North Carolina State (4-1) bounced back from its first loss of the season, a four-point setback to Oklahoma State last Sunday.
North Carolina-Asheville (1-5) was led by Jeremy Atkinson with 28 points.