Hill's score put LSU ahead 23-14 -- enough of a cushion to withstand a late Gamecocks touchdown.
Hill finished with 124 rushing yards and two scores on 17 carries.
Zack Mettenberger completed 12-of-25 passes for 148 yards with an interception for the Tigers (6-1, 2-1 SEC).
The victory was an NCAA Division I-best 22nd straight at home for LSU.
Connor Shaw was intercepted twice en route to 177 yards and two touchdowns for the Gamecocks (6-1, 4-1), whose school-record 10-game winning streak was snapped.
2014: The Year in Music [PHOTOS]