C.J. Williams ran for a 12-yard score with 1:31 left in the first half after Lee Marvel intercepted a pass from Ed Achziger. Bucknell (2-0) forced a three-and-out from Marist and Nitti drove Bucknell back down the field quickly, capping the drive with a 12-yard touchdown pass to Will Carter with one second left in the half and giving the Bison a 19-0 lead.
A 35-yard fourth-quarter field goal by Derek Maurer, who missed a field goal on the game's opening drive, sealed the win for Bucknell.
Williams ran for 161 yards on 27 carries. Nitti was 21-of-31 passing.
Marist (0-2) was held to 19 yards rushing on 24 carries. Achziger threw for 119 yards.