Down 54-52, Britt's layup tied the game at 54 with 3:08 remaining. Thornton then scored four straight points -- a layup and two free throws -- to put William & Mary ahead 58-54 with 1:59 left.
Towson managed just two points in the final 2 minutes while William & Mary converted five free throws in the same span to seal the victory.
The Tribe made 12 free throws for the game compared to four for the Tigers.
Marcus Damas scored 13 points and grabbed seven rebounds for the Tigers (10-12, 5-4), who have now lost three straight.