Kip Patton ran for a 13-yard to score to put Temple up 21-12 in the fourth.
In the second half, Temple (9-2, 6-1 American Athletic Conference) held Memphis (8-3, 4-3) to a field goal and twice ended Memphis drives with punts and turnovers on downs. Memphis' final drive ended as time expired.
The Owls retained first place in the conference's east division.
Paxton Lynch was 25-for-34 passing for 156 yards for the Tigers.