Garret Covington scored four points during an 8-1 run that put Western Illinois (7-3) up 66-65 with under six minutes to play.
Owens found Adekoya for a 3-pointer then hit a jumper before assisting on Devon Friend's layup that put Chicago State up by six with 1:42 left.
The Cougars made 5 of 6 free throws down the stretch to seal the win.
Covington led Western Illinois with 21 points and J.C. Fuller scored 17.
The game featured 21 lead changes and seven ties. Two free throws by Owens with eight seconds left capped the scoring and gave Chicago State the game's biggest lead by either team.