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.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.