The teams met in the semifinals of the NIT Season Tip-Off, which concludes on Friday with Michigan facing Kansas State in the championship game.
Michigan made 8-of-8 from the foul line over the final 1:22 with Stauskas hitting half of those shots. Trey Burke's two free throws with 2 seconds remaining clinched the victory, Michigan's fourth in four games this year.
Burke led the Wolverines with 17 points, Tim Hardaway Jr. added 16 and Stauskas had 15.
Pittsburgh (4-1) owned a seven-point lead in the second half before stumbling down the stretch. The Panthers got 14 points from Lamar Patterson.