Davis was 7 of 10 from beyond the arc.
Andre Nation had 10 points for the Dukes (14-11, 8-4 Colonial Athletic Association), who have won four of five.
JMU outscored William and Mary 30-14 in the paint and 25-0 off turnovers.
The Tribe led 11-6 early, but the Dukes tied it at 30-all at halftime.
Behind of three 3-pointers from Davis and a three-point play by Moore, JMU led 53-41 with 12:09 remaining. Davis made another 3-pointer at 10:42 for 56-43 advantage.