Randolph threw for 422 yards and three touchdowns, including the game-winner to Koster with six seconds left. Matt Partain's extra point provided the winning margin.
Brett McDermott and Nick Cole caught touchdown passes from Randolph for Holy Cross (7-3, 5-0 Patriot League). McDermott had eight catches for 107 yards and Jon Brock added six catches for 122 yards for the Crusaders.
Lafayette (7-3, 3-2) held a 13-7 halftime lead and extended it to 20-7 early in the third on a 2-yard touchdown run by DeAndre' Morrow.
But the Crusaders responded with a 23-yard field goal by Partain later in the third and a 32-yarder early in the fourth. Cole's 22-yard touchdown catch tied the score at 20 with 5:36 left.
Morrow scored on a 22-yard run with 2:45 left, but a missed extra point kept the Leopard lead at 26-20 and gave Holy Cross the chance to win.
Morrow finished with 111 yards on 15 carries and Marc Quilling threw for 184 yards and a touchdown for Lafayette.
Holy Cross outgained the Leopards 490 total yards to 330.
Maria Taylor and Peter Burns share the greatest moments of the year around the conference.
SEC Network looks back at all of the NCAA Championships won by the SEC this year.
SEC Network's Summer Tour stops by Baton Rouge to visit with Les Miles and the Tigers.
Three-time NFL MVP quarterback Brett Farve shares his stories of coaching high school football at the LSU Coaches Clinic.
SEC Network looks back at the highs and lows of Tigers' season.
Baylor has released five signees from its 17th-ranked recruiting class, including J.P. Urquidez, Kameron Martin, Donovan Duvernay and Patrick Hudson. Sources said the other was Parrish Cobb.