The Bulldogs (7-2) shot 43.9 percent from the field (25 of 57) and overcame 17 turnovers to win their third game in three days.
Alabama State (1-8) shot just 29 percent from the field (18 of 62) and hit only 6 of 27 3-pointers.
Ravern Johnson, Mississippi State's leading scorer, was suspended for the game for violating the school's class attendance policy.
The Bulldogs opened the game on a 15-6 run but trailed 28-26 at the half. Mississippi State recovered early in the second half and controlled the game from there.
Bailey was 4 of 8 from the field and 5 of 8 from the free-throw line. He also had seven rebounds.
Bryant hit 4 of 7 shots from the field, and Benock hit 4 of 7 -- including 3 3-pointers -- and had six rebounds.
Kenderek Washington paced the Hornets with nine points.
Sidney is eligible to return Dec. 18 against Virginia Tech, and Bost will be eligible for the start of Southeastern Conference play in January.
Both will play in Wednesday's exhibition game against Belhaven in Jackson, Miss.