Stone posted 22 points and 11 rebounds while Layman added 18 points and 10 boards as the Terps (15-2, 4-1 B1G) saw its nine-game winning streak snapped.
Michigan (13-4, 3-1 Big Ten) led by as many as 13 points in the second half, but the Terrapins came all the way back behind Stone, who scored 19 after halftime. Maryland took a brief lead at 57-56, but the Wolverines made enough big shots down the stretch.
Michigan led 67-59 after a pair of 3-pointers, but Maryland made one last run. Stone cut the deficit to two when he made two free throws with 40 seconds left, but after a Michigan miss at the other end, the Wolverines came up with the decisive offensive rebound.
Rasheed Sulaimon's tying attempt from beyond the arc missed.
Robert Carter added 15 points for Maryland, which welcomes Ohio State for a noon tilt on Saturday at XFINITY Center.