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.
Coach Gilmore on CWS win: 'It's indescribable' Coastal Carolina head coach Gary Gilmore reflects on his 21 years as head coach and is proud of how far the program has come.
Two late June events provided a great start on the 2020 class and a look at some new 2019 talent.
ESPN Recruiting Insider Jeff Borzello discusses how Terrance Ferguson's decision to play basketball internationally will impact his positioning in the 2017 draft, as well as the Wildcats' upcoming season.