McDermott was 29 of 40 for 322 yards passing for the Mustangs (6-3, 4-2 Conference USA), and Line compiled 143 yards on the ground.
Ryan Griffin threw for 214 yards and two TDs for the Green Wave (2-8, 1-5).
Tulane trailed 31-0 at halftime, but Griffin rallied it to within 38-24 at the end of the third quarter. Early in the fourth quarter, the Green Wave marched to the SMU 25 when Griffin fumbled, and Chris Banjo recovered for the Mustangs.
That was Tulane's last gasp, and SMU clinched the game by driving 75 yards in 12 plays to McDermott's 2-yard touchdown pass to Terrance Wilkerson.
Darius Johnson had seven catches for 135 yards and a TD for the Mustangs.