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.
Notable deaths of 2014 [PHOTOS]