Guidugli ignored temperatures that dipped into the low 20s, completing 25 of 37 passes for 231 yards as the Bearcats finished the season at 7-5.
Marshall overcame an early 10-0 deficit with two quick touchdowns in the opening period and did not score the rest of the contest.
Guidugli threw touchdown passes to Earnest Jackson and Brent Celek after Derrick Haitchcock opened the scoring by returning a blocked punt 10 yards in the game's opening minute.
Marshall quarterback Stan Hill completed 14 of 30 for 137 yards and a touchdown.
The Thundering Heard closed at 6-6.