Will Barton had 14 points, 10 rebounds and four steals for the Tigers (12-5, 3-0 Conference USA), and Tarik Black chipped in 10 points, six rebounds and five blocked shots. Memphis was 34 of 61 (56 percent) from the field.
Memphis dominated from the outset, opening the game on a 12-4 run. Houston pulled to 13-9 after Harris hit two free throws 11:50 before halftime, but that set off another big Memphis run.
Houston got within 47-39 five minutes after halftime, but the Tigers put the game away with an 18-0 run.
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.