Geron Johnson added 19 points and Joe Jackson chipped in 17 points and 10 assists for the 20th-ranked Tigers (27-4, 16-0 C-USA), who won their third game in a row and ended the season undefeated in conference play.
Memphis led 43-28 at halftime and was 16-of-23 from the free-throw line.
Jordan Swing scored 19 points and Rod Rucker scored 16 for UAB (15-16, 7-9), which ended its season with two consecutive losses.
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