Hayes gave Memphis (5-3, 3-1 American Athletic Conference) a 20-14 lead with a 51-yard run with 14 seconds left in the first half and added 30- and 14-yard scoring runs in the fourth quarter.
Tulsa (1-7, 1-3) opened the scoring with 6 seconds left in the first quarter on Demarco Nelson's 6-yard fumble return, and took a 14-3 lead in the second on Dane Evans' 28-yard pass to Derek Patterson. Memphis rallied on Lynch's 3-yard run and Elliott's 37-yard field goal.
Evans also threw a 1-yard scoring pass to Keyarris Garrett with 6 minutes left in the fourth quarter.
Evans was 28 of 54 for 349 yards. Keevan Lucas had 11 catches for 120 yards.