The Bulldogs (11-8, 2-4) led much of the game with first place in the SEC West on the line, but faltered at the end of each half in the loss to the Gamecocks (12-8, 2-4).
Brandon Wallace, a former Silver Bluff standout, scored 10 points for South Carolina and tied a career-high with 16 rebounds. Jamont Gordon led Mississippi State with 16, but disappeared in the second half as Kelly asserted himself. Gordon missed a 3-pointer as time expired.
Mississippi State has lost six of its past eight, but remains in the jumbled SEC West chase.
The Bulldogs led by as much as 12 in the first half and seven in the second half, but went cold over the final 18 minutes.
Wallace led the Gamecocks back from a seven-point deficit in the middle of the second half with five points in an 11-2 run that gave South Carolina its first lead since the opening minutes. His emphatic dunk in transition ended the run and gave his team a 55-53 advantage with 9:18 left.
Mississippi State built a 12-point lead with a 14-3 run early in the first half that included five points from Ben Hansbrough, who scored 11. But South Carolina got back in the game by holding the Bulldogs scoreless over the final 3:55 of the half and trailed 36-35 at halftime.
South Carolina, which never led by more than four, got 15 points from Dwayne Day and Charles Rhodes added 10 for Mississippi State.
ARKANSAS 63, NO. 12 ALABAMA 57
IN TUSCALOOSA, ALA., Patrick Beverley scored 19 points and Arkansas dominated Alabama for 30 minutes before hanging on to win.
The Razorbacks (14-7, 3-4 Southeastern Conference) outmuscled Alabama in the paint as 7-footer Steven Hill pulled down 16 rebounds. Arkansas held a seemingly insurmountable 51-27 lead with 10:50 to play when the Crimson Tide started their rally and outscored the Razorbacks 30-12 the rest of the way.
Alabama (15-5, 2-4) was led by Richard Hendrix, who had 28 points and 11 rebounds and sparked the comeback with several thunderous jams.
VANDERBILT 85, MISSISSIPPI 80
IN NASHVILLE, TENN., Derrick Byars scored 19 points and three other Commodore players scored in double figures as Vanderbilt beat Mississippi.
Clutch foul shooting down the stretch helped the Commodores hold off a furious second-half rally by Mississippi (13-8, 2-5).
Vanderbilt (15-6, 5-2) hit seven-of-eight free throws in the game's final 2:22.