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.
ESPN's Dan Dakich joins The Paul Finebaum Show to discuss the SEC's presence in the NBA Draft.
Ted Kapita was the top-rated recruit from West Virginia in the class of 2015 and recently played at DME Academy in Florida.
With the Suns drafting Tyler Ulis, they now have five guards on their roster who attended Kentucky.