Moore was 9 of 16 from the field and Daniels hit 7 of 10 shots.
Beau Beech made five 3-pointers and finished with 17 points for North Florida (8-4). Trent Mackey added 13 points on four 3s as the Ospreys made 41 percent of their 39 3-point attempts.
Florida International led 29-28 before North Florida closed the half on a 17-7 spurt for a 45-36 halftime advantage. Beech made three consecutive 3-pointers early in the second half for a 16-point lead.
Adrian Diaz had 19 points and seven rebounds for FIU (4-6). Cameron Smith added 11 points and 12 boards. The Golden Panthers outrebounded North Florida 49-34 but made just 4 of 15 from 3-point range and missed 10 of their 22 free throws.