The Rattlers (1-6) were led by Reggie Lewis with 13 points.
North Florida opened the second half with a 7-2 spurt for a 46-32 lead on David Jeune's layup 1:42 in and pushed it 59-36 on Wallace's layup midway through the half.
The Ospreys' lead never dipped below 19 points from there.
Florida A&M made the first bucket, but when North Florida's Cameron Naylor made two foul shots, the Ospreys led 18-8 with 12:50 left. North Florida maintained at least an eight-point lead and made it 39-23 on Charles McRoy's dunk with 1:45 left.
The Rattlers cut it to 39-30 at halftime.