Dudash completed 17 of 24 passes with no interceptions for the Seawolves, who hadn't beaten Georgetown in their previous three tries. Mason carried 22 times for 173 yards.
Stony Brook had 564 yards of total offense.
Bassuener made it 21-13 with a 4-yard run 4:33 before halftime and Lane's 5-yard pass to Nick Parrish early in the third quarter made it 21-19 before Charlie Houghton ran in a 2-point conversion to tie it.
But Dudash completed a 3-yard pass to Chris Tyler with 5:52 left in the third and Mason followed with a 3-yard run early in the fourth.