The Buckeyes built a 10-point halftime lead, then scored the first nine points of the second period to win their ninth in a row and set up a third-round meeting with Iowa State. The Cyclones advanced with a 76-58 decision over Notre Dame.
Ohio State, the No. 2 seed in the West Region, forced 18 turnovers and shot 47 percent from the field.
Thomas scored 24 points while Thompson added 20 to go with 10 rebounds. Lenzelle Smith contributed 12 points for the Buckeyes (27-7), who defeated Iowa, Michigan State and Wisconsin to win the Big Ten Tournament last week.
Iona (20-14) reached the tournament by capturing the title game of the Metro Atlantic Athletic Conference. The Gaels began that tourney as the No. 4 seed.
Tavon Sledge scored 20 points to lead Iona and Sean Armand had 17.