The Bobcats responded with a 55-yard drive that ended with Green's 38-yard field goal with 8:08 remaining. The defense then forced a three-and-out and Ohio ran the clock down to 1:23 when Green connected for 22 yards.
Xavier Hughes picked off Thompson to seal the win.
Oklahoma moved up to No. 3 behind Clemson and Alabama and the Big Ten placed three teams in the top six of the new Associated Press college football poll.
Stanford, USC, Cal and Oregon were among the Pac-12 programs with key recruits in on Rivalry Week.
Georgia's recruits reacted quickly and sharply to Sunday's news that Mark Richt would step down after 15 seasons with the Bulldogs.
After failing to crack the top 100 nationally in total offense over the past two seasons, John Donovan was fired as offensive coordinator at Penn State.
Here is a list of the FBS head coaching changes made during the 2015 season.
Oklahoma State and West Virginia were among the Big 12 programs that had key recruits on campus this weekend.