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.
DouDou Gueye, a 6-foot-10 center from Senegal, has signed with Ball State as a graduate transfer from South Carolina State.
We have changes at the top of the draft and a shakeup in the lottery, with teams starting to make their final decisions. Get the latest in Chad Ford's Mock Draft 9.0.
Duke freshman point guard Derryck Thornton Jr. is transferring to USC, his father announced on Friday to Scout.com.