The Knights (4-6) had the lead only briefly before going into halftime tied at 33 and fell behind for almost the entire second until closing the game on a 6-0 run.
Fairleigh Dickinson inbounded with 25.1 seconds left trailing by one and ran the clock down until Townes got the ball on the left wing with eight seconds left. Townes drove to the elbow, hesitated, then cut to the basket, finishing with a reverse right-handed scoop off the glass.
The Knights defenders caused a loose ball scrum in the final seconds to secure the win as Towson (7-4) tried to answer going the other way.
Malik Miller led five Knights in double figures with 12 points.
Byron Hawkins had 16 points to lead Towson.