Ryan Tentler threw a 78-yard pass to Kegan Moore, who made it to the 1 to set up Mazza's scoring run on the ensuing play, putting the Hatters up 15-14 with 14:55 left to play after trailing 14-8 at halftime.
The Red Foxes (3-7, 3-4 Pioneer League) then went three-and-out and Stetson got the ball at the Marist 38. A 9-yard run from Washington stretched the lead.
Marist had one more chance to score, but Anthony Francis was sacked and fumbled on fourth down and the Hatters (5-5, 3-3) controlled the ball for the final 2:24 to seal the win.
Francis threw for 114 yards and two touchdowns to lead Marist.