Matt Grothe threw for 338 yards and two touchdowns for USF (3-0) which overcame a 17-point deficit to take a two-touchdown lead before Kansas' Todd Reesing tied the game with two fourth-quarter TD passes.
Reesing had the Jayhawks on the move again when safety Nate Allen intercepted his deep throw in the middle of the field and returned it 40 yards to the Kansas 27 with 30 seconds remaining.
Bonani, making his college debut, kicked the game-winner two plays later.
Grothe won the matchup of undersized quarterbacks who elevated their teams into the national spotlight with TD passes of 21 yards to Taurus Johnson and 37 yards to A.J. Love during an 18-minute stretch in which USF outgained the Jayhawks 346 yards to 15 to climb out of its big hole and take a 34-20 lead.
A week after throwing for a career-best 412 yards against Louisiana Tech, Reesing went 34-of-51 for 373 yards and three touchdowns. Johnathan Wilson caught two TD passes and finished with nine receptions for 160 yards, while Kerry Meier had 11 catches for 120 yards for Kansas.
The Jayhawks and Bulls were two of college football's biggest surprises of 2007, with both climbing as high as No. 2 in the country before dropping out of contention for a spot in the BCS championship game.
This season is about establishing that they can be major players on the national stage for years to come.
Kansas lost for just the second time in 16 games with Reesing as its starting quarterback, the other a neutral-site loss to Missouri. The Jayhawks scored on their first two possessions, building a 10-0 lead, and Reesing's 4-yard TD run made it 20-3 late in the second quarter.
