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Pierce took a lateral from quarterback Austin Davis and threw the touchdown pass to give Southern Miss a 37-30 lead with 12:35 left in the game.
The Golden Eagles (6-3, 3-2 Conference USA) increased their lead to 39-30 when Cordarro Law hit Green Wave quarterback Ryan Griffin, who fumbled the ball out of the end zone for a safety with 2:23 remaining.
Southern Miss completed the scoring when Alexander Walters forced and recovered a Devin Figaro fumble and ran 41 yards for a touchdown with 21 seconds remaining.
Tulane (3-6, 1-4) outgained the Golden Eagles 402-358 and had 11 more first downs (28-17).