The Buckeyes outscored the Tigers 42-18 in the opening 20 minutes, during which Thomas scored 21 of his 22 points. Having outscored Savannah State by himself during the first half, Thomas played only 10 minutes of the second period.
Ohio State improved to 7-1 by winning its 37th straight game against non-conference opponents.
LaQuinton Ross added 13 points and nine rebounds for Ohio State, which hit 10-of-19 from 3-point range. Ohio State has run off three straight wins since dropping a decision to Duke on Nov. 28.
The Tigers (5-5) were led by Arnold Louis with 14 points.