The Buckeyes compiled a 9–2 record, including the 1973 Rose Bowl in Pasadena, California, where they lost 42–17 to the USC Trojans.
Ohio State was the only team to beat the Tar Heels in 1972.
Ohio State made two goal line stands, one in each half, to hold on to the 14–11 victory.
In the fourth quarter, Randy Gradishar stopped Franklin on a sneak from the one.
The Buckeyes' fans tore down the goal posts with 13 seconds remaining.