Goodwin's slam with 42.5 seconds left in overtime gave Memphis an 80-77 lead, and the Tigers (21-6, 10-4 AAC) held on down the stretch for a fifth win in six games.
Austin Nichols supplied 17 points, 12 rebounds and seven blocks.
Will Cummings posted 24 points the Owls (7-19, 2-12). Quenton DeCosey netted 23 and Dalton Pepper added 20 for Temple.
Swim Week Miami Beach 2014 [PHOTOS]