Green was 14-of-26 passing for 213 yards with an 18-yard touchdown pass to Willie Johnson and added a rushing touchdown. Knox rushed for 113 yards on 25 carries and scored twice.
The Herd (7-3, 5-1), who won their fifth straight, moved into a tie with Florida Atlantic atop the East standings. The Bulldogs (8-2, 5-1), who hadn't lost since falling to Texas in their season opener, are a half-game ahead of Southern Mississippi in the West.
Louisiana Tech opened the scoring with a 5-yard run by Justin Henderson, but a field goal and the touchdown pass put Marshall on top in the second quarter. In the final minute of the first half, Kevin Murphy recovered a fumble by Brady Farlow at the La Tech 1 and Knox punched it in with 40 seconds to go for a 17-7 lead.
The Bulldogs kicked a field goal in the third quarter but that was all they could manage.
Marshall piled up 405 yards of offense, while La Tech was held to 261.
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