Goodwin was 15 of 23 from the field and made all four of his free throws.
Central Florida cut it to 89-82 with 1:34 left but Memphis made 6 of 7 free throws to seal it.
Avery Woodson hit five 3-pointers and scored 19 points, and Ricky Tarrant Jr. added four 3s and 18 points for Memphis (13-7, 4-3 American), which made 12 of 23 from 3-point range. Dedric Lawson added 15 points, 12 rebounds and five assists.
Goodwin had 24 points, seven rebounds and five assists in the first half as Memphis built a 54-40 lead. The Tigers made 22 of 42 shots, including 7 of 12 from distance.
Justin McBride made all eight of his shots and scored 20 points for UCF (10-8, 4-3).