Johnson led all scorers in the game with 22 points. She also dished out five assists as MSU improved to 11-5 overall, 1-2 in SEC play.
Porsha Porter made it a two possession game as she closed the contest with a pair of free throws. The Chicago native scored 16 points on the night, pushing her past the 500-point mark for her career.
Alabama led 41-34 at halftime thanks to five three pointers and 12-of-15 from the free-throw line. State's defense stiffened over the final 20 minutes, though, holding Alabama off the charity stripe and scoreless from beyond the arc.
Catina Bett joined her three teammates in double figures with 11 points.
Alabama (10-8, 0-4 SEC) was paced by 15 points from Celiscia Farmer and 11 points each from Jasmine Robinson and Kyra Crosby.
The Lady Bulldogs return home Sunday, hosting No. 16 Georgia for Alumni Day. Tip at Humphrey Coliseum is set for 2 p.m.