The score was tied at 7-all when Albert McClellan forced a fumble by Tulane's Jeremy Williams and Hall picked up the football and ran into the end zone with 41 seconds left in the first quarter.
The Thundering Herd (4-2, 2-1 Conference USA), pulled away from there, using a goal-line stand and three more takeaways to hold the Green Wave in check and win for the third time in four games.
Marshall running back Darius Marshall rushed for a season-low 98 yards and two touchdowns on 20 carries.
The Green Wave (2-3, 0-2) saw its two-game winning streak snapped. Andre Anderson led Tulane with 92 yards on the ground.