The Buckeyes improved to 4-0 while hitting 59 percent of their field goal attempts and making good on 9-of-16 from 3-point range.
Thomas scored 21 points while Lenzelle Smith had 13 points and 10 rebounds.
Ohio State opened the game on a 20-3 run and stormed to a 53-18 lead at halftime. Missouri-Kansas City (2-3) made only 14 field goals for the entire game, shot 25 percent and missed all of its 14 attempts from beyond the arc.
The Kangaroos were led by Estan Tyler and Thomas Staton with seven points each.