Lattimore toted the ball 23 times while Connor Shaw hurled two touchdown passes as the Gamecocks (5-0, 3-0 SEC) notched their school record-tying ninth straight victory dating back to last season.
Shaw, who went 15-of-18 through the air for 148 yards, also ran the ball 19 times for 76 yards.
Kentucky (1-4, 0-2) suffered a blow when starting quarterback Maxwell Smith was forced to leave early in the first quarter after suffering an ankle injury.
Jalen Whitlow took over and threw for 114 yards with two interceptions on 12-of-23 efficiency.
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