Craft scored the Buckeyes' final seven points, including a buzzer-beating trey that handed Ohio State (28-7) a second NCAA victory following a first-round defeat of Iona.
The junior guard finished with 18 points and six assists while DeShaun Thomas added 22 points and grabbed five rebounds as the Buckeyes stayed hot with a 10th consecutive overall win.
Making its fourth Sweet 16 appearance in four years, Ohio State now goes on to face sixth-seeded Arizona at Thursday's West Regional in Los Angeles.
The 10th-seeded Cyclones (23-12) were led by Korie Lucious with 19 points and four assists.
Will Clyburn chipped in with 17 points and four boards for Iowa State.