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.
Vince Young headlines College Football Hall of Fame inductees
Former Texas quarterback Vince Young, along with former Notre Dame receiver Raghib Ismail and one-time Arkansas running back Darren McFadden, headlined the list of 13 players and two coaches inducted into the College Football Hall of Fame on Tuesday.
Two suspended Cornhuskers facing sexual-assault-related charges
Nebraska's Katerian LeGrone and Andre Hunt face felony charges after their arrests Tuesday. LeGrone was booked on a charge of first-degree sexual assault, and Hunt was booked on a charge of first-degree aiding and abetting sexual assault.
Utah State QB Jordan Love declares for NFL draft
Jordan Love, the No. 7-ranked draft-eligible quarterback, according to ESPN NFL draft analyst Mel Kiper Jr., announced Tuesday that he's leaving Utah State to enter the draft.
Colorado Buffaloes receiver K.D. Nixon declares for NFL draft
Colorado junior receiver K.D. Nixon will forgo his final season of eligibility to enter the NFL draft. Nixon's move follows that of fellow receiver Laviska Shenault Jr., who announced last week that he is declaring for the draft.
Nevada players disciplined for brawl against UNLV
The Mountain West Conference has suspended DB Austin Arnold, DB Daniel Brown and DT Hausia Sekona for the Famous Idaho Potato Bowl as a result of their roles in a brawl against UNLV on Nov. 30. In addition, LB Gabriel Sewell is banned for the first half.
New Mexico to pay $825K buyout to Bob Davie
New Mexico will pay former football coach Bob Davie an $825,000 buyout over the next 30 months. School officials said the money for the Davie buyout will come from future game guarantees.