Hampton (11-11, 6-3) had a double-digit lead for long parts of the first half, but Morgan State (8-12, 6-2) took lead late in the second half.
Hampton bounced back to force overtime when Ramon Mercado hit a 3-pointer to tie the game at 70 with 3.5 seconds left.
The Pirates led during the end of the first overtime, but Morgan State's Donte Pretlow tied the game at 80 on two free throws with 3.2 seconds left.
Morgan State took command in the second overtime when Blake Bozeman -- the son of Bears coach Todd Bozeman -- made two free throws and followed with a 3-pointer for a 90-85 lead with 25.5 seconds left.
Hampton's Brian Darden cut the lead to 93-92 on a late 3-pointer, but the Pirates couldn't do anything else.
Du'Vaughn Maxwell led Hampton with 25 points and 11 rebounds.
The teams shot 115 combined free throws.