Thompson was 5-of-7 from the field and was one of four Ohio State (8-1) starters to reach double figures in the Buckeyes' fourth-consecutive victory.
Lenzelle Smith was also sharp from the field, scoring on 7-of-10 shots and totaling 12 points and seven rebounds.
Keith Hornsby hit 6-of-8 3-point shots and tallied 26 points for UNC-Asheville (3-7), who had won their last two contests coming into Saturday's game.
Both teams were sharp from the field. Ohio State shot 59 percent and the Bulldogs shot 42.4 percent.
The Buckeyes outscored the Bulldogs 50-35 in the first half and out-rebounded the visitors 31-26 for the game.