The game went back and forth until William & Mary pulled ahead on a pair of McDowell free throws with 4:47 left, and increased it to 63-58 on McDowell's layup just over a minute later.
Charles Jenkins went 2-for-2 from the free throw line to pull Hofstra within three, but McDowell and Schneider hit a combined nine foul shots to seal it for the Tribe down the stretch.
Steven Hess added 12 points for the Tribe (14-3, 6-1 Colonial Athletic Conference), who shot 51.1 percent from the floor (24-for-47).
Jenkins scored 19 to lead the Pride (9-10, 2-5), who shot 37.5 percent (24-for-64).
The Tribe, who have won four straight, kept pace in a three-way tie with George Mason and Northeastern atop the CAA.