Hitchens hit five 3-pointers en route to 6 of 9 shooting for the Dukes, who snapped a five-game losing skid.
James Madison (11-16, 4-11 Colonial Athletic Association) started hot, opening the game on a 25-8 run and taking a 36-21 lead into halftime behind an Andrey Semenov layup.
Towson (1-26, 1-14) rallied in the second half to take its first lead of the game, 51-49, with 3:20 left to play but Hitchens made a trey and Moore scored the Dukes' final six points to seal the win.
Despite dominating the boards 49-19 the Tigers shot just 27.6 percent (16 of 58) from the field.
James Madison shot 45.5 percent (10 of 22) from 3-point range.
Robert Nwankwo led Towson with 15 points and 15 rebounds.
- James Madison
- Colonial Athletic Association