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 guard prospect was one of the top players at the annual Spiece Run N Slam event.
SMU has signed a second player from Australia, 6-foot-11 forward Harry Froling, to a national letter of intent. The Mustangs previously signed guard Tom Wilson from Australia.
There's nothing to suggest the Jayhawks won't end up atop the Big 12 for a 13th season in a row. But what about a return to the Final Four?