The win snaps a two-game skid for the Bulldogs (15-7, 6-2 Southeastern Conference) and guarantees the team will continue to hold at least a share of the lead in the SEC Western Division.
It's the Bulldogs' first season sweep of Alabama in nine seasons.
Despite trailing most of the second half, Alabama (13-10, 2-6) pulled to within two points on an Alonzo Gee field goal at the 3:20 mark. But Jarvis Varnado answered after a missed shot by Alabama and put the Bulldogs back up by four, securing the win.
Mississippi State led 33-29 at halftime, built mainly on Stewart's eight first-half points and Gordon's six early assists.
The Bulldogs shot 48 percent in the contest and held Alabama to just 36 percent from the field.