The Tar Heels blew open the game early with a 22-4 run to take a 27-8 lead midway through the first half.
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.
When the long-range shots didn't fall, North Carolina simply rebounded and scored. The Tar Heels finished the game with more offensive rebounds (22) than McNeese State's total for defensive rebounds (21), scoring 21 second-chance points.
The Cowboys, meanwhile, struggled to score. They shot 36 percent from the floor in each half, making 3 of 17 3-point attempts in the game.
McNeese State managed only one field goal, a jumper by McFerrin, during a seven-minute stretch in the first half as the Tar Heels pulled away.