Nassib, who finished with four TD passes, all coming in the second half, marched the Orange (4-4, 3-1 Big East) 75 yards in 1:20 for the winning score. He had helped cut Syracuse's deficit to 33-31 on a TD pass to Marcus Sales, a 19-yarder with 7:17 left.
After blowing a 23-3 halftime advantage, USF (2-6, 0-4) regained the lead, 26-24, on Maikon Bonani's 41-yard field goal with 2:15 left in the third. The Bulls went up 33-24 just over four minutes into the fourth when B.J. Daniels threw a 30-yard TD pass to Andre Davis.
Bonani's school-record fifth field goal of the game, a 47-yarder, made it 36-31 with 1:27 remaining. The Bulls have lost six games in a row.
Nassib, the Big East passing leader, completed 27 of 40 passes for 328 yards. Jerome Smith rushed for 127 yards on 28 carries for the Orange.
USF had won six of the seven previous meetings between the teams since joining the league in 2005, with the lone loss against the Orange coming home at Raymond James Stadium two years ago. The Bulls have dropped 12 of their last 13 Big East games dating to November 2010, with the only victory over that stretch coming against Syracuse.
The Bulls took a late lead over unbeaten Louisville last week, only to watch the Cardinals come from behind in the closing minutes to win 27-25. USF also faltered late in the four losses previous to this game and last week's.
The Bulls rushed for 369 yards, including 145 from Lindsey Lamar and 134 by Daniels, against a Syracuse defense that had given up just 35.3 yards per game on the ground against league opponents.
Demetris Murray had a 1-yard TD run on USF's opening drive of the game and Bonani added a 35-yard field goal as South Florida took a 10-3 lead after one quarter.
Lamar broke free for an 80-yard touchdown run to make it 20-3 in the second quarter just one play after Syracuse's Ross Krautman missed a 22-yard field goal.
Nassib started the second half comeback with a 31-yard scoring strike to Jarrod West early in the third. After Lemon had a 4-yard TD run, Nassib then connected with Sales on a 5-yard TD to put Syracuse up 24-23 midway through the third.