The Wolverines (6-17, 2-9 Big Ten) broke a six-game losing streak and picked up their second win of 2008. Penn State (11-12, 3-8) has lost eight of nine, its lone win being a Feb. 2 upset of then-No. 8 Michigan State.
Anthony Wright added 13 for Michigan, including 10 in the first half.
Michigan led 32-26 at the half but fell apart coming out of the break. The Wolverines went scoreless for nearly six minutes while Penn State was scoring 12 straight points to go up 38-32.
The Nittany Lions led 50-44 with 10:31 to play, but the Wolverines came back with a nine-point run capped by a Harris fast-break dunk.
The lead went back and forth until Battle's free throw tied the game at 57 with 4:08 left.
Baskets by Ekpe Udoh and Sims gave Michigan a four-point edge, but Udoh missed the front end of a one-and-one with 2:49 to go.
After two free throws by D.J. Jackson, Udoh was called for offensive goaltending with 2:00 to go, but the Wolverines got a key stop.
Harris increased the margin to 64-59 with a three-point play, but two Jackson free throws made it a three-point game with 51 seconds left.
Penn State started to foul, and after Sims made two from the line, Udoh clinched the game with a spectacular block.