Maine opened the game score on its first three possessions, and left the first quarter leading 21-7.
The Gamecocks would score again at the beginning of the second quarter, before Maine would score another three touchdowns itself.
Scoring would flip flop until the end of the game when Ramon Jefferson scored his second touchdown, sealing Maine's first playoff win since 2013.
Jefferson finished with 26 carries for 201 yards and two touchdowns.
Quarterback Chris Ferguson completed 14 of his 26 pass attempts for 159 yards five touchdowns.
The "black hole" Maine defense accounted for four sacks, two fumbles and an interception in the win.
Maine will travel to Weber State for their quarterfinal matchup next Saturday.