The Buckeyes, seeded second, will meet No. 1 seed Syracuse Saturday to determine which will advance to the Final Four.
Ohio State led by 12 at halftime, fell behind by three points with 12 minutes remaining and then outscored the Bearcats 32-14 the rest of the way.
Sullinger was overwhelming inside, scoring 23 points and grabbing 11 rebounds. Thomas had three 3-pointers among his 24 points. Ohio State came up with 13 steals and made 14 more free throws than did Cincinnati.
Only six players scored for Ohio State, which shot 49 percent from the floor. The Buckeyes will take a 30-7 record into its meeting with Syracuse.
Cincinnati (26-11) got 18 points from Cashmere Wright before he fouled out. Sean Kirkpatrick added 15 points for the Bearcats, the region's sixth seed.