David Jeune added a team-high eight rebounds for the Ospreys (10-15, 5-7), who have now defeated Kennesaw State eight straight times.
North Florida dominated inside, outscoring Kennesaw State 32-18 in the paint.
The Owls (2-21, 1-10) took a 9-0 lead to open the game but North Florida responded with a 20-3 run to take a 20-12 advantage with 7:39 remaining in the half. The Ospreys maintained the lead the rest of the game.
Markeith Cummings, who is tied with Smith for first in scoring in the A-Sun Conference, matched his season average with 17 points for Kennesaw State. Cummings was the only player in double figures for the Owls, who have now lost eight straight games.