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.
Arizona linebacker Scooby Wright's left knee injury is not season-ending, according to an MRI Wright had after Thursday night's opening win over UTSA, sources told ESPN's Brett McMurphy.
Syracuse starting quarterback Terrel Hunt has a significant injury to his right Achilles, head coach Scott Shafer said after the Orange's season-opening 47-0 rout of Rhode Island.
The Mountain West told ESPN's Brett McMurphy that officials correctly ruled the final play that kept Colorado from getting a potential game-tying touchdown against Hawaii before time expired.
ESPN 300 running back Elijah Holyfield, the son of former heavyweight boxing champion Evander Holyfield, has decided to stay home and attend Georgia, he announced Friday.
Miami reserve linebacker Al-Quadin Muhammad has been suspended for the season opener against Bethune-Cookman on Saturday for a violation of team rules, a source confirmed to ESPN.com
Ohio State quarterback Cardale Jones is "doing fine" after he was released from the hospital Wednesday night after being treated for symptoms related to a migraine headache.