Ohio St. will be given credit for it but they're not really the first FBS team to do it after a playoff. What is considered as part of the regular season now was once a playoff in its inception. And that was the 1992 SEC Championship won by Bama who in turn went on to defeat Miami in the Sugar Bowl for the '92 National Championship.
After beating runner-up Melvin Gordon and 3rd-place finisher Amari Cooper, Ohio State is a win over Marcus Mariota away from becoming the *first team in college football history* to BEAT each of the top three Heisman vote-getters in a single season.
I think this game was the national championship game, if Bama played the ducks they would have beaten them as well. Alas we will never know. In saying that I'm a Buckeye Alum and very proud of my Buckeyes. Two national championships in the 21st century, and yes " The future looks bright at Ohio State.".