The Tigers (13-6, 4-1 Conference USA) trailed 36-35 with 13 minutes to play, but outscored the Mustangs 19-2 over the next 11 minutes to pull away.
During a stretch of the second half, SMU (10-9, 2-3) connected on only 2 of 18 shots to help Memphis build a double-digit lead.
Memphis controlled the boards 36-27, including 13 off the offensive glass, leading to 14 second-chance points.
Memphis had 9-point lead, 30-21, in the first half but SMU closed out the period with seven straight points to lead 30-28 at the break.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.