The Cardinals (9-1) were trailing 54-44 with under 12 1/2 minutes before Behanan sparked a comeback in which Louisville outscored the Tigers 43-24 down the stretch.
Peyton Siva collected 19 points to go with seven assists and Russ Smith also scored 19 as the Cardinals racked up their fourth consecutive victory.
Memphis (6-3) got 23 points from Joe Jackson and Tarik Black added 21 but also committed eight turnovers as the Tigers saw their four-game winning streak snapped.
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