The Hornets tied the game for the final time at 50-50 with 2:37 remaining on Stephawn Brown's 3-pointer from the top of the key.
Savannah State took the lead for good with just over two minutes to play and extended it to 55-51 with 1:18 left in the game on a 3-pointer by Williams. A three-point play by Joshua Freelove brought the Hornets (0-4) to within one at 55-54 with 55 seconds remaining, but the Tigers (3-1) held on for the victory.
Freelove led Alabama State with 17 points.
Savannah State led 9-2 and 19-6 in the first half, but Alabama State came back to within two, trailing 25-23 at the break.