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.
With a trio a top recruits from Philadelphia, the Penn State basketball program is primed to finally turn a corner.
Maryland point guard Melo Trimble, considered a lock to leave the program before struggling in the second half last season, has withdrawn from the NBA draft and will return for his junior season.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.