The Bobcats (29-7) became the first No. 13 seed to reach the round of 16 since Bradley in 2006. They did it with a big contribution from D.J. Cooper, who provided 19 points, seven assists and six rebounds.
Ohio will now face top-seeded North Carolina in Friday's Midwest Regional semifinal game.
Twelfth-seeded South Florida (22-14) fell despite 13 points and 10 rebounds from Victor Rudd Jr.
Anthony Collins also contributed 13 points and Augustus Gilchrist provided 12 and five rebounds in the Bulls' loss.