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.
LSU QB Joe Burrow wins Maxwell and Davey O'Brien awards
Joe Burrow, the favorite to win the Heisman Trophy on Saturday, won the Maxwell Award and the Davey O'Brien Award Thursday night at the 2019 Home Depot College Football Awards in Atlanta.
Chase continues LSU's run with Biletnikoff nod
Ja'Marr Chase wins the Fred Biletnikoff Award for the nation's most outstanding receiver as LSU runs away with the 2019 CFB Awards.
Burrow wins Maxwell Player of the Year Award
Joe Burrow says he idolizes how Drew Brees plays quarterback after winning the Maxwell Award.
Duffy delivers another Ray Guy Award for the Aussies
Kentucky's Max Duffy has been named the most outstanding punter in college football, bringing the accolade "home" to Australia.
Blankenship becomes UGA's first Groza winner
Senior Rodrigo Blankenship reflects on his emotional journey en route to winning the Lou Groza Award as college football's best kicker.
Delpit brings Thorpe Award back to DBU
LSU safety Grant Delpit lets his play speak for itself by taking home the Paycom Jim Thorpe Award as the nation's best defensive back.