Paxton Lynch was 21 of 28 for 230 yards for the Tigers (6-3, 4-1 American Athletic). Mose Frazier had eight catches for 110 yards, and Brandon Hayes ran for 75 yards on 26 carries and had two catches for 24 yards.
Memphis took a 13-10 lead on Elliott's 27-yard field goal with 1:39 left in the third quarter.
Temple opened a 10-0 lead in the first quarter on Jones' 43-yard field goal and Kenneth Harper's 75-yard run. Memphis tied it in the second on Elliott's 42-yard field goal and Lynch's 17-yard pass to Hayes.
P.J. Walker was 17 of 39 for 145 yards for the Owls, and Harper finished with 116 yards on 17 carries.