Alabama trailed early in the second half, but three-balls from Anthony Brock and Torrance, sandwiched by a Johnson jumper, began a 17-4 run with Senario Hillman's layup giving the team a 46-34 lead a little less than nine minutes in.
However, Romero Osby stopped the bleeding with a jumper and that kick-started 14 straight points by Mississippi State with Stewart's three-pointer giving the team a 48-46 lead with 7 1/2 minutes left.
'Bama, though, tied the game on two free throws from Green, Brock gave the team the lead with a three-pointer and Chris Hines followed with a layup for a 53-48 lead with 4 1/2 minutes to play.
Johnson put in a layup with 1:27 to play to cut the Bulldogs' deficit to 56-55, but Torrance followed with two from the line.
After Phil Turner put in a layup, Brock hit two free throws with 16 seconds to play and, after Stewart turned the ball over, Green made two more free throws to seal the win.
The Tide scored 12 of the first 14 points of the game with Torrance's three- ball making it a 12-2 game just over two minutes in.
Alabama maintained a significant lead through the next several minutes, but the Bulldogs closed the half with a 13-3 run and Bost's jumper just before the buzzer got his team to within one-point, 27-26, after 20 minutes of play.
Mississippi State plays at Arkansas on Thursday...Alabama hosts LSU on Wednesday...Alabama owns a 112-71 lead over Mississippi State in the series, and these teams will meet again on February 24.