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.
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Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.