The victory snapped a four-game losing streak for the Pirates (13-6, 2-4 Big East). The Bulls (10-8, 1-5) lost for the fifth time in six games.
Mobley, who returned to action after missing one game with a separated shoulder, scored eight of his points in the second half to hold off any possible South Florida run. The Bulls twice got to within six in the second half.
The Pirates never trailed, scoring the first five points and pushing their lead to double digits twice, the latest being 29-19 with 43 seconds left in the half.
Poland's long 3-pointer at the buzzer sliced the lead to 29-22 at the half.
The first half was played at a slow, methodical pace.
After the Pirates led 5-0, then later 12-4 on a layup by Edwin, the Bulls crawled back to trail 14-13 after a layup by Zach LeDay with 10:46 left in the first half.
But the Pirates went on a 9-0 run for a 23-13 lead with 6:01 remaining in the half. Teague had six of the nine Seton Hall points during that stretch.
South Florida scored the first six points of the second half to slice the lead to 29-28 with 16:10 left on a power move from Martino Brock.
But Edwin scored the next five points, a 3-pointer and two free throws, to push the lead back to 34-28 with 15:10 remaining.
Mobley, who missed the Marquette game last week as a result of his separated shoulder, had two power dunks that gave the Pirates a 38-32 lead with 12:40 left.
Brian Oliver, who also just returned to action after missing five games with a sprained ankle, canned a 3-pointer from beyond the top of the key to push the Pirates' lead to 41-32 with 11 minutes remaining.
Mobley added another power move down low, giving the Pirates their largest lead at 45-34 with 9:40 left.
Edwin had 10 rebounds. Seton Hall held South Florida to 33.9 percent shooting (19 of 56) and 15.8 percent (3 of 19) from 3-point range.