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.
Michigan coach Jim Harbaugh said Tuesday he has informed competing quarterbacks Jake Rudock and Shane Morris of his decision on a starter for the Wolverines' opener Thursday night at Utah.
Michigan State quarterback and Heisman Trophy hopeful Connor Cook said he was disappointed his teammates didn't vote him among the team's three captains this season.
Former Oklahoma State return man and running back Ty Hill, who was dismissed from OSU's program after his arrest on domestic violence charges, has enrolled at West Alabama.
A months-old Facebook post has cost the Nebraska football stadium announcer his job one day after his hiring was announced.
UCLA junior cornerback Ishmael Adams has been suspended indefinitely following a robbery arrest early Sunday morning, coach Jim Mora said Tuesday.
No. 5 Michigan State will start redshirt freshman Vayante Copeland at one of its two cornerback spots Friday night at Western Michigan.