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.