Freshman Nik Stauskas led the Wolverines (6-0) with 20 points and Tim Hardaway Jr. added 16, but it was Burke who controlled the game, equaling his previous career high of nine assists in the first half and going the whole game without a turnover.
N.C. State (4-2) trailed 73-58 before going on a 10-0 run capped by T.J. Warren's layup with 2:11 remaining. Hardaway answered with a driving bank shot.
It was 75-70 when the Wolfpack forced a turnover and called a timeout with 54.4 seconds to play, but C.J. Leslie was called for an offensive foul.
Leslie appeared to swing his left arm a bit while backing down against Michigan's Mitch McGary. N.C. State coach Mark Gottfried was incensed by the call on the sideline.
Warren led the Wolfpack with 18 points.
Michigan committed only six turnovers—four in the first half. N.C. State shot 57 percent from the field but lost its fifth straight game in the ACC-Big Ten challenge.
Michigan led 45-40 after Leslie's twisting dunk early in the second half. The Wolverines answered with an alley-oop pass to Glenn Robinson III, whose dunk popped out of the basket momentarily before dropping back in.
Michigan methodically built its lead into double digits and led 62-48 after Stauskas made a 3-pointer from the right wing.
It was 73-58 before N.C. State made a game of it down the stretch. Warren scored on a 3-on-1 break to make it 73-68. He was fouled on the play but missed the free throw that would have cut the deficit to four.
Michigan has committed 10 or fewer turnovers in five of its six games this season.
Before the game, Michigan raised a banner commemorating its 2012 Big Ten regular-season title—the program's first since 1986. The Wolverines look even more dangerous so far this season, especially when they're moving the ball well and making outside shots.
Stauskas made his first four shots—three from 3-point range—as part of a 13-point first half. One of Stauskas' 3-pointers gave Michigan a 30-16 lead, but the Wolfpack went on a 7-0 run to get back in the game.
N.C. State shot 60 percent in the first half but trailed 43-36 at halftime after Burke drove to the basket and made a nice pass to Robinson for a layup in the waning seconds.
Burke finished the half with no points and nine assists.
Stauskas went 4 of 7 from 3-point range in the game and is 14 of 24 on the season.