Corey Allen Jr. also finished with 18 for South Florida (11-10, 2-6, American Athletic Conference), which made its last 15 free throws to seal the victory. Perry, the four-time conference rookie of the week, added a team-high eight rebounds.
Nic Moore scored 23 points to lead SMU (16-5, 5-3), which was outscored in the paint for the first time this season (38-28). Ben Moore and Markus Kennedy each had 11 points and Nick Russell added 10 for the Mustangs.
Both teams began slowly with only two field goals apiece midway through the first half. South Florida led 30-29 at the break after five lead changes. There were a dozen more after the intermission.
Early in the second half, Rudd hit a pair of free throws to tie the game at 35 and become the 18th player in school history to reach the 1,000-point mark.
The loss for SMU ended a five-game winning streak that began with a 71-54 rout of USF in Dallas. The Mustangs were seeking to go 13 games over .500 for the first time since the 1999-00 season.
South Florida finished with a 14-2 scoring advantage off the fast break and 27-21 in bench points.
The Bulls won for only the third time in 11 games, after an 8-2 start, and snapped a four-game home losing streak.