Dixon finished with 11 points overall for the Tigers (18-5), who snapped the Bulldogs' seven-game winning streak with the comeback victory.
Chris Crawford (11 points), Shaq Goodwin (10, eight rebounds) and Joe Jackson (10, four, five assists) also played key roles for Memphis.
Gonzaga (21-4) got 18 points and eight rebounds from Sam Dower.
Gerard Coleman and Przemek Karnowski chipped in 12 points apiece.
Swim Week Miami Beach 2014 [PHOTOS]