The Buckeyes remained unbeaten in their nine games this season, holding the Bulldogs to 27 percent shooting and forcing 19 turnovers.
Smith made 6-of-9 shots from the field, two of them coming from 3-point range, while Amir Williams added 12 points.
Ohio State owned a 20-point lead at halftime.
Bryant, in its fifth year as a Division I basketball program and playing in the Northeast Conference, was led by Dyami Starks with 16 points.
Ohio State came into this week's action having allowed the third fewest number of points per contest in the NCAA. The Buckeyes were giving up 54.5 per game, behind only Clemson (53.6) and Western Illinois (54.1).