Mississippi State (4-7) opened with a 14-3 run and led 33-25 at the half.
But Alabama A&M (4-7) held the Bulldogs scoreless for the first 7 minutes, 22 seconds of the second half and eventually took a 35-33 lead.
The lead changed several times throughout the rest of the half, and with 43 seconds remaining, Green Hill hit a layup to give Alabama A&M a 58-57 lead. After a failed possession by Mississippi State, Hill hit another free throw to seal the win.
Brandon Ellis added 13 points for Alabama A&M.
Craig Sword paced Mississippi State with 14 points, and Gavin Ware added 12 points and 11 rebounds, his second consecutive double-double.
Jalen Steele scored 10 points for Mississippi State in his first game back from a wrist injury on Nov. 13.