Taylor Bessick nearly had a double-double with nine points and 13 rebounds for the Dukes (9-8, 3-1 Colonial Athletic Association), who won their second straight game.
The score was tied at 38-all with 4:43 left in the second half after Dartaye Ruffins' 3-pointer. But James Madison pulled away with a 10-0 run to claim a 48-38 advantage, holding Drexel scoreless for four minutes.
Moore completed a three-point play and made two free throws during the James Madison spurt.
Frantz Massenat scored 11 points for the Dragons (5-11, 1-3), who lost their third consecutive game.
James Madison shot 37 percent (17 of 46) from the floor, while Drexel made 36.2 percent (17 of 47) of its shots.
The family of former Houston Astros owner Roy Hofheinz wants a court to require the University of Houston to keep his name on the school's basketball arena.
Michigan has hired assistant basketball coaches Billy Donlon and Saddi Washington.
Duke and Cincinnati, 2016 NCAA tournament teams, highlight the eight-team field for the Naismith Memorial Basketball Hall of Fame Tip-Off Tournament.