Jelani Hewitt hit a 3 with 4:33 to play, giving Georgia Southern (4-2) a 58-55 lead, but the Eagles would go 0 for 6 from field from that point.
Daiwuan Walker hit a 3 to tie it 16 seconds later and, after a stop on the other end, he made 1 of 2 free throws to give UCF a 59-58 lead with 3:11 remaining.
Trent Wiedeman made the first of two free throws to pull Georgia Southern even at 59 with 1:05 left.
Brandon Goodman missed a 3, but Wilson's tip-in dunk gave UCF the lead for good.
Hewitt, who finished with 17, missed 3-pointer in the closing seconds.