Iowa (17-15) will move on to face fifth-seeded Wisconsin (23-8) in the second round on Thursday.
Payton Sandfort finished with 17 points for the Hawkeyes, who shot 55% (29 of 53). Josh Dix added 16 points and Pryce Sandfort had 10. Harding shot 5 of 6 from the floor and made three 3-pointers.
Thornton scored 24 points and had nine assists to lead Ohio State (17-15). Devin Royal chipped in with 17 points and Micah Parrish had 16.
There were 13 lead changes and the score was tied 10 times. Iowa shot 10 of 24 from 3-point range while Ohio State was 5 of 22 from distance.
The teams were tied at 37 at the break then Iowa opened the second half on a 17-9 run for its largest lead at 54-46, with about 14 minutes remaining. The Hawkeyes took the lead for good, 62-61, with 7:11 to play.
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