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.
Maryland point guard Melo Trimble has withdrawn from the NBA draft and will return to College Park for his junior season, sources told ESPN.
Louisville's Chinanu Onuaku, who recently underwent a medical procedure to correct a heart rhythm issue detected during the combine, will keep his name in the NBA draft pool.
Andrew White III will return to the Nebraska men's basketball team next season after removing his name from the NBA draft.