Desmond Jackson added 12 points as the Bulldogs (6-8, 3-2 Southwestern Athletic Conference) shot 52.9 percent from the field (27 of 51) and outrebounded the Hornets 35-22.
Alabama A&M broke a nine-game losing streak to Alabama State (5-13, 2-3).
The Bulldogs led 39-32 at halftime and extended the lead to 49-37 on Tabb's free throw with 14:28 left. Jackson's 3-pointer gave Alabama A&M a 54-39 advantage with 13:11 to play.
Casey Cantey added 10 points for Alabama A&M.
Chris Duncan scored 17 points and Tramaine Butler added 13 points and five steals for Alabama State, which shot 50 percent from the field (10 of 20) in the second half, but only 52.2 percent from the free-throw line (12 of 23) for the game.