Cornley paced the Nittany Lions (15-5, 4-3 Big Ten) early, burning the Wolverines on an assortment of short jumpers and layups.
Penn State led by 23 by midway through the second half, when Battle and backcourt mate Stanley Pringle combined for five 3-pointers to help the Nittany Lions pull away.
Michigan couldn't recover from a cold spell in the first half, when they shot just 30 percent from the field (9 of 30), including 2-of-16 from 3-point range.
Battle got the best of Michigan's Manny Harris (four points) in a matchup between the Big Ten's top two scorers.
DeShawn Sims scored 21 points to lead the Wolverines (13-6, 3-4), who lost their third straight.