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.
Florida State's student government has passed a resolution discouraging Seminoles fans from wearing Native American headdresses at games.
The second annual Gavitt Tipoff Games, eight games between members of the Big East and Big Ten to be played Nov. 14-18, will feature Villanova at Purdue in the opener.
Michael Lewis is leaving his assistant coaching job at Butler to take the same position at Nebraska under Tim Miles.