The Nittany Lions mounted a comeback bid in the third period but fell short.
Ryan Barker's walk-off overtime field goal completed Penn State's comeback.
The Nittany Lions secured their first series sweep of the season against Union.
Singleton is Penn State's leading rusher with 53 carries, 408 yards, and three touchdowns.
The Nittany Lions are 4.5-point favorites for the cross-country battle.
The Nittany Lions failed to register a shot on target as they suffer a third Big Ten loss in Bloomington.