McDonald led the charge, scoring all of his points in the first half. He made his first two shots, both of which were 3-pointers, during the decisive run.
Jeremie Mitchell scored 13 points to lead the Cowboys (6-4), whose five-game winning streak ended.
Craig McFerrin added 10 points for McNeese State, which dropped to 0-4 against teams from the Atlantic Coast Conference.
The Tar Heels bounced back from an 85-67 loss at Texas on Wednesday night in which they shot 31 percent from the field, made 3 of 19 3-pointers and committed 18 turnovers.
North Carolina's 3-point shots fell early and often against McNeese State. Marcus Paige began North Carolina's 22-4 spurt with a 3-pointer, and Bullock ended it with a 3-pointer.
The Tar Heels shot 54 percent from the field in the first half, including 8 of 17 from 3-point range, en route to a 54-23 lead at halftime.
North Carolina took advantage of a porous zone defense by McNeese State. The Tar Heels whipped the ball around the perimeter to generate open looks, recording 18 assists and three turnovers in the first half.