Davis scored the first eight UCF points of the second half as the Knights took their first double-digit lead at 37-25. UCF led by 13 points midway through the half until Chris Perry's layup cut it to 52-48 with three minutes left.
Shaheed Davis and A.J. Davis combined to score the next seven points for a 59-48 lead. The duo scored UCF's final 12 points.
Shaheed Davis finished with 15 points for UCF (10-6, 4-1 American). A.J. Davis made 12 of 14 free-throw attempts as the Knights hit 25 of 32 compared to 4 of 11 for the Bulls.
Perry led USF (3-17, 0-7) with 18 points and eight rebounds. Jahmal McMurray added 15 points for the Bulls, who have lost nine in a row.