Aldrick Robinson scored on a 96-yard touchdown reception to tie for the longest touchdown pass in SMU history, and the Mustangs (3-2, 2-0 Conference USA) snapped the Pirates' five-game conference winning streak.
The Mustangs are 2-0 in conference play for the first time since 1986 when they played in the Southwest Conference.
Dominique Lindsay led all rushers with 144 yards on 24 attempts for ECU (3-3, 2-1).
The Mustangs scored 21 consecutive points to take a 21-7 lead, capped by safety Rock Dennis' 53-yard interception return with 8:12 left in the third quarter.
Dennis' TD followed the record-tying play by Robinson and Mitchell. Robinson caught the ball near midfield before outrunning two East Carolina defenders to score at 11:07 of the third quarter. In 1982 quarterback Jeff Courtwright connected Craig James on a 96-yard TD pass against North Texas.
SMU's first score came on a 63-yard touchdown return by Bryan McCann off a blocked field goal by Sterling Moore with 3:52 left in the first half. SMU's Margus Hunt blocked another field goal attempt earlier in the game.
Mitchell threw a 17-yard touchdown pass to Terrance Wilkerson with 5:02 left in the game to give SMU a 28-14 lead. East Carolina pulled to within 28-21 after Dwayne Harris, who scored the game's first touchdown on a 10-yard run, returned ensuing kickoff 77 yards for a TD with 4:42 left. ECU had a chance to tie the game, but Patrick Pinkney threw an incomplete pass on fourth-and-26 from the SMU 38 yard with 41 seconds remaining.