Carl Wilson's 15-foot jumper with 30 seconds left -- the only points scored in the second overtime -- gave the Trojans the victory in Petersburg, Va.
With two seconds remaining and Ousmane-Ba at the foul line for the Bison, Mike Hampton committed a lane violation on the first attempt -- which was good -- and the ball went over to Virginia State to seal the victory.
Howard trailed, 71-60, with 6:39 left in regulation before scoring 12 straight points to take a 72-71 lead, following Robert McIlwaine's follow-up basket with 3:59 to play. Fred Hill had eight of the points in the run.
The Bison led, 77-75, following Hampton's free throw with 37 seconds left. But Keith White's 10-foot jumper for the Trojans forced the overtime.
In the first overtime, Hampton scored all five of Howard's points and the Bison had a chance to win with the game tied at 82, but Fred Hill missed a jumper from the top of the key to send the game into the second overtime.
Virginia State (9-13) was led by Alfred Cantrell's 20 points. Howard (13-11) was led by Hampton's 24 points and Hill's 21.