Beech and Banks combined to make 16 of 21 field goals and grabbed eight rebounds apiece.
After trailing by as many as 15, a 3-pointer by Darion Green pulled Edward Waters within six, 39-33, with 1:58 left in the first half.
North Florida scored the final eight points, including six by Moore, to take a 47-33 lead into halftime and Edward Waters never threatened again.
Nathaniel Hill led the Tigers with 29 points and 13 rebounds while Green finished with 21.
The game served as an exhibition for Edward Waters.