Omar Cooper Jr.'s go-ahead toe-tap touchdown in the final minute sealed Penn State's sixth consecutive loss.
Dominick Stewart was red hot for the Nittany Lions, going 6-8 from deep.
Backup quarterback Jaxon Smolik will miss his second straight game.
The Nittany Lions will play their first home game without James Franklin since 2013.
Penn State will miss the Big Ten Tournament in back-to-back years.
Penn State takes their first loss in conference play against the top-ranked Spartans.