Kelly, a freshman, made the kick at 1 a.m. after failing on two other attempts that could have won the game.
Michael Robinson threw for 253 yards on 21-of-39 passing with a touchdown and an interception for the Nittany Lions (11-1). Reserve tailback Austin Scott, replacing an injured Tony Hunt in the first quarter, rushed for 110 yards and two scores for Penn State. Jordan Norwood caught six passes for 110 yards, while Ethan Kilmer had 79 yards and a touchdown on six grabs in the win.
Drew Weatherford went 24-of-43 for 258 yards with a touchdown and an interception for the Seminoles (8-5).
FSU kicker Gary Cismesia missed two field goals in overtime and an extra point in the second quarter.
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