Ashley Adams added 14 points, six blocked shots and four assists for the Buckeyes (2-1), who have won 23 consecutive home games, the longest active streak in the Big Ten.
Ohio State jumped out to a 14-2 lead in the first meeting between the two programs.
Ahead 31-20 with 3:43 left until the break, the Buckeyes closed out the half on a 12-0 run.
Ohio State, which has now hit at least one 3-pointer in 122 straight games, was 7 of 14 from long range compared to 4 of 16 for the Eagles (1-1).
The Buckeyes also had the advantage at the free-throw line, making 17 of 26 attempts while Winthrop was only 5 of 6.
Dequesha McClanahan and Diana Choibekova scored 12 apiece for the Eagles.