Webber, from Babson Park, Florida, stayed with the Ospreys through the first half and took a one-point lead at the half, 31-30.
The Warriors opened the second half with a 3-pointer by Jovany Deceus, but North Florida responded with a 12-0 run and pulled away throughout the second half.
Moore was 9 of 12 from the field, 4 of 5 from three-point range, to finish with 22 points. Davenport was 7 of 11 from the field and drilled his only three-point attempt to finish with 18.
As a team, the Ospreys shot 28 of 48 from the field (58.3 percent) and out-rebounded Webber 34-17.
Deceus was 6 of 9 shooting to finish with 14 points and was the only Webber shooter to reach double figures.