Miller completed 15-of-22 passes and ran for 77 yards for the Buckeyes (1-0), who are coming off an undefeated 12-0 season.
Jordan Hall ran for 159 yards and two TDs for Ohio State.
Buffalo (0-1) rallied for two touchdowns in the second quarter -- one on a 47-yard interception return by Khalil Mack -- and trailed 30-13 at halftime.
Joe Licata threw two TD passes for the Bulls, who are playing in their 100th football season.
Puzzle-maker slips 'Murdoch Is Evil' into Rupert Murdoch's Sunday Telegraph
Wisconsin business offering 'therapeutic cuddling' forced to close