Eugene Harvey added 19 points and six assists while Nutter finished with 16 for the Pirates (13-14, 4-10 in Big East), who had lost their last five games.
The win also snapped an eight-game losing streak against Big East teams and kept Seton Hall's conference tournament hopes alive. To earn the 12th and final seed, the Pirates must win their final two games against Cincinnati and Louisville, both on the road, and St. John's must lose its final conference game against Providence on March 4.
McHugh Mattis led South Florida (12-16, 3-11) with 21 points, while Kentrell Gransberry had 19 points and 12 rebounds and Melvin Buckley scored 16 points for the Bulls, who have not won on the road in their two seasons in the Big East.
Seton Hall took the lead for good when Nutter hit consecutive 3-pointers to give the Pirates a 59-56 lead with 12:30 remaining, spurring a 14-5 run.