The Tigers (42-14) improved to 19-11 in the league. They will finish no worse than tied for the top, depending on what happens in later games involving Kentucky and Florida.
LSU's victory marked the second time in three seasons South Carolina (39-15) watched an opponent celebrate an SEC crown on its home field.
The Gators did that in 2010 when they won two of three in a showdown series with the Gamecocks.
The Tigers staged a two-out, two-run rally in the 10th to win. Slaid's single brought in Jordy Snikeris to break a 1-1 tie and Mason Katz followed with an RBI single.