Ohio State (21-11) advances to play top-seeded and third-ranked Michigan in the quarterfinals on Friday.
Thornton had a personal 10-0 run to give Ohio State its largest lead of the game at 51-35 with 13:55 remaining.
But Iowa rallied down the stretch to get within 70-69 with 38.7 seconds left.
Ohio State worked the clock down before Thornton drove into the lane for a shot that rolled off the rim. Amare Bynum‘s putback attempt did not go, but Ohio State secured the rebound, and Mobley was fouled before making two free throws for a three-point lead with 8 seconds left.
Iowa got past midcourt to call a timeout with 7.2 left. Brendan Hausen‘s 3-point attempt from the corner did not hit the rim, but Iowa got another chance after Ohio State missed the front end of a 1-and-1.
Iowa forward Alvaro Folgueiras missed a free throw in the closing seconds, but Isaia Howard stole the rebound and ran out to the 3-point arc for a shot that hit off the back of the rim as time expired.
Bennett Stirtz led Iowa (21-12) with 17 points.
Up next
Ohio State lost both regular-season meetings with Michigan by double figures, most recently an 82-61 contest at home on Feb. 8.
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