The Cougars (7-8, 3-1 Ohio Valley), who had a five-game win streak broken earlier in the week, rebounded to beat Tennessee State (3-15, 0-3).
SIU-Edwardsville had climbed into a 38-38 tie and Tennessee State called time with the ball and 1:46 to play. The Tigers' Christian Mekowulu missed a jumper after the huddle with Nunn grabbing the rebound only to miss a layup at the other end.
The Cougars won the rebound battle and the ball kicked out to Davis, who drained a 3-pointer from the corner with 1:02 to play. Nunn stole the ball and ran it in for a layup with 37 seconds left. He added a pair of free throws with 26 seconds remaining.
Mekowulu led the Tigers with 12 points and 12 rebounds.