Glenn Robinson III added 14 points and seven rebounds while Jordan Morgan chimed in with 10 points and 10 boards for the second-seeded Wolverines (26-8), who won seven straight games before falling to rival Michigan State in the finals of the Big Ten Tournament.
The Wolverines will meet the winner of Arizona State and Texas in the Midwest Region third round.
Karl Cochran had 17 points to pace 15th seed Wofford (20-13) in defeat, as the Terriers shot just 1-for-19 from behind the arc.
After Lee Skinner opened the game with a pair of easy buckets for a 4-0 Wofford advantage, the Terriers missed 10 straight shots. Michigan failed to take advantage, however, scoring just nine points during that stretch. The Wolverines led 9-6 at the second media timeout.
The Maize and Blue pushed the spread to 25-14 behind Stauskas, who hit his first three shots from the floor for seven points after playing the role of facilitator early on.
Robinson had seven in the final three minutes of the stanza, and a pair of Stauskas free throws gave Michigan a 34-20 lead at halftime.
Stauskas went over the 1,000 point mark for his career with a corner 3-ball to open the second half.
The Terriers pulled to within 40-33 near the midpoint of the second half after Cochran's triple capped 13-2 surge. Morgan's timely three-point play restored a double-digit margin for Michigan.
LeVert's trey from the top of the key with 4:19 to play ended all hopes of a Wofford comeback.