Hill's go-ahead score capped a 10-play, 79-yard drive that came after Odell Beckham had tied it up with an 88-yard punt return for a touchdown as LSU (9-2, 5-2 SEC) rallied from a 35-28 fourth-quarter deficit.
Hill ended the day with 86 rushing yards.
Zach Mettenberger shook off two late interceptions to finish 22-of-37 for 282 passing yards as the Tigers won a second straight following a loss to Alabama.
LSU keyed the victory by turning four Ole Miss turnovers into 13 points.
Bo Wallace was intercepted three times for Mississippi (5-6, 2-5), overshadowing his 310 yards and four TD passes on 15-of-35 attempts.
Donte Moncrief amassed 161 receiving yards with two scores on six grabs for Ole Miss.