The Golden Lions (2-8) scored their first road victory in seven tries while handing the Cougars (5-2) their first home loss in five games.
Arkansas-Pine Bluff led 27-16 at halftime and was up 16 points with 15:29 left in the game before Houston scrambled back, tying the game with 36 seconds left on two free throws by LeRon Barnes. Neither team scored in regulation after that.
The Lions scored the first eight points of overtime. Houston got within three with 30 seconds left after a free throw and grabbed an offensive rebound, but Tevin Hammond made a steal and Mosely hit four free throws down the stretch to get the win.
JoVaughn Love had 10 rebounds for the Lions.
Jherrod Stiggers led Houston with 16 points. Barnes added 14 points and 12 rebounds.