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 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. A double-teamed Gordon missed a 3-pointer as time expired.
Mississippi State has lost six of its last 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.
South Carolina outscored Mississippi State 11-8 from there. Kelly scored six of those points to put the game away.
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.
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