The game-winner came after Savannah State's John Barron missed a 44-yarder on the first possession in overtime.
The Spartans (3-6, 3-3 Mid-Eastern) prompted the extra session with 10 fourth-quarter points, on Shakeem Copeland's 2-yard touchdown run and Marouf's 41-yard field goal with 2:28 left.
Savannah State (1-7, 1-5) went up 17-7 in the third on Arshon Spaulding's 1-yard plunge which capped an 11-play, 79-yard drive.
Spaulding ran for 97 yards on 18 carries and was 5 of 9 passing. Richard Williams III added 87 yards rushing with a 3-yard touchdown run.
Norfolk State's Greg Hankerson was 18 of 35 for 131 yards and 46 yards rushing, while Copeland had 56 yards on seven carries.