Evans threw an 18-yard touchdown pass to Keyarris Garrett to put Tulsa up 7-6 in the first quarter, and the Hurricane's went on to lead by as many as 22 points, 35-13, with just over 5 minutes to play in the third.
Garrett finished with 96-yards receiving and two touchdowns, and Zack Langer added 167 yards on the ground for Tulsa (2-7, 2-3 American).
Matt Davis had two short TD runs to close SMU's deficit to seven in the fourth quarter.
The Mustangs currently rank 128th - last in the FBS - in both average points scored (7) and allowed (48) this season.
Davis threw for 212 yards and one touchdown, and ran for another 181 yards and two touchdowns for the Mustangs (0-8, 0-4).