Adrian Edwards added 13 points and 10 rebounds, both career highs, for Alabama A&M (5-12, 4-3 Southwestern) and Rakiya Battle had a career-high 12 assists.
LeAntwan Luckett's putback off his own blocked layup with 12:34 to play pulled Alcorn State (4-16, 3-5) within 52-44, but the Bulldogs scored the next 10 points to push their lead to 18 about three minutes later.
The Braves used an 11-1 run to cut their deficit to 70-62 with three minutes remaining, but got no closer.
Marquis Vance scored 17 points for Alcorn State, which made just 10 of 38 (26.3 percent) field goals, including 2 of 10 from 3-point range, and 9 of 22 free throws in the second half.
Alabama A&M made 27 of 54 from the field.