Scott Wood added 14 points, including a pair of clutch jumpers in the final 3 minutes that helped NC State hold on.
Jeremy Atkinson scored a career-high 28 points for the Bulldogs, who lost their fifth straight since beating Western Carolina in the opener.
This looked like a game that would give NC State the chance to regroup after a 20-point loss to Oklahoma State in the Puerto Rico Tipoff championship game on Sunday. Instead, NC State's struggles continued against an aggressive and opportunistic bunch of Bulldogs who wouldn't go away.
While NC State shot 56 percent for the game, it committed 19 turnovers that UNC Asheville converted into 31 points. Meanwhile, the 6-foot-4 Atkinson frustrated the Wolfpack the entire way by being quick enough to get his shot off the dribble or muscle around in the paint. NC State tried freshmen Rodney Purvis and T.J. Warren on Atkinson before turning to junior C.J. Leslie in the final minutes.
After the Wolfpack took the 70-69 lead on Howell's basket, Wood followed with a straightaway jumper that pushed the lead to four. Two possessions later, Wood answered a 3-pointer by Trent Meyer with one of his own, losing Keith Hornsby around a screen on the right wing to make it 76-72 with 1:16 left.
UNC Asheville got as close as 80-78 on a three-point play from Hornsby with 16.5 seconds left, but Howell made it a two-possession game with his free throws and the Bulldogs managed a meaningless putback just before the buzzer to end it.
NC State improved to 18-0 all-time against UNC Asheville, led by former Wolfpack player Eddie Biedenbach.