Robbie Gould kicked three first-half field goals for the Nittany Lions (2-4, 2-3 Big Ten), who have won two straight after an 0-4 start.
The early-season slump kept Paterno from reaching the 324 victories he needed to pass legendary Alabama coach Bear Bryant. Paterno tied Bryant's record of 323 last week in a 38-35 triumph at Northwestern.
Early in the second half, it did not look good for Paterno as Derek Ross returned an interception 45 yards for a score, increasing Ohio State's lead to 27-9.
But Mills answered on the ensuing possession, racing 69 yards for a touchdown. He later found Tony Johnson from 26 yards and Eric McCoo from 14 yards, giving the Nittany Lions a 29-27 lead 13 seconds into the fourth quarter.
Mills carried 15 times for 138 yards and completed 17 of 32 passes for 280 yards with three interceptions. Penn State had three of the game's five turnovers to offset 531 yards of total offense.
The Buckeyes (4-3, 2-2) scored on their first play from scrimmage as Steve Bellisari threw a 66-yard touchdown pass to Michael Jenkins 2:41 into the game to open the scoring.
Mike Nugent answered Gould's field goals with a pair of his own and Ohio State took a 13-9 edge into the locker room.
Jonathan Wells then broke off a 65-yard touchdown run on the second play from scrimmage in the second half, increasing the lead to 20-9. Ross' defensive touchdown was Ohio State's final score.
Wells rushed 19 times for 143 yards, but Bellisari went just nine of 21 for 209 yards with an interception. Jenkins had four catches.
After the game, Paterno addressed the sellout crowd by saying he was most proud, "of this football team."
"This is going to be a heck of a football team," Paterno said.