The victory ran the Buckeyes' winning streak to 18 games.
With starting quarterback Craig Krenzel sidelined with a strained elbow on his throwing arm, Coach Jim Tressel went back to basics this week in practice.
The result was an effective running game as Ross rushed for 94 yards and two touchdowns on 22 carries, and Hall added 107 yards on 19 attempts. The Buckeyes (4-0) ran for 205 yards after averaging just 102 yards in their first three games.
The Falcons got a 33-yard field goal by Shaun Suisham with 1:46 remaining to cut it close.
"We once again allowed someone at our place to have a chance in the fourth quarter and that is something that we've got to straighten out," Tressel said.
Bowling Green reached the Ohio State 48 on its final possession, but safety Will Allen sealed the win with an interception. Last week, he made a game-saving tackle at the goal line against N.C. State, and has a 100-yard interception return two weeks ago against San Diego State.
"It's a loss; it stinks," said Bowling Green Coach Gregg Brandon. "Ultimately, in sports it's win or lose. This is a great game to learn from."