Kilgore was 22 of 40 for 277 yards and four touchdowns for the Blue Raiders (4-4, 2-2 Conference USA). Jefferson had seven catches for 91 yards, and Jordan Parker ran for 127 yards and a touchdown on 21 carries.
Marshall scored two late touchdowns to take the lead. Kevin Grooms scored on a 1-yard run with 8:17 to go, and Essray Taliaferro put the Thundering Herd up 49-45 with a 2-yard run with 2:29 left.
Kilgore then drove the Blue Raiders 79 yards for the winning score, also completing passes of 24, 14, 5 and 18 yards to Jefferson on the 13-play march.
Kilgore threw two 16-yard touchdown passes in the first half, connecting with Kyle Griswould in the first quarter and teaming with Christian Collis to tie it at 21 with 27 seconds left in the second. Kilgore had a 1-yard scoring run in the third quarter and threw a 6-yard TD pass to Corey Carmichael early in the fourth.
The latest defensive triplets to be featured are Colorado's, as the Buffaloes are ranked ninth and could go even higher if their defense improves more.
Ohio State hits the road on Sept. 17 to take on Oklahoma, which returns QB Baker Mayfield and RB Samaje Perine after averaging 43.5 points in 2015.
The San Francisco 49ers made DeForest Buckner a first-round pick this year and will pair him with another former Oregon star in Arik Armstead.
The Horned Frogs are among the top teams in the Big 12. If Arkansas can beat them, it'll say something about how far Bret Bielema's team has come.
If you're not a preseason Heisman favorite, you need to grab the nation's attention with big plays in big games. Here are the games where 10 hopefuls can make their mark on the Heisman race.
With so much uncertainty at offensive tackle, the Boilermakers will be counting on newcomer Jalen Neal to make an immediate impact.