After yielding 44 points in LSU's only loss of the season at Georgia two weeks ago, and 23 points in the first half at Mississippi State last week, the Tigers' defense kept an opponent out of the end zone for the first time this season.
Tyler Murphy passed for 115 yards for the Gators (4-2, 3-1), who led 3-0 early, but managed just one more field goal on the day.
Murphy was sacked four times by an LSU defense that finished with eight tackles for losses.
Florida made it a one possession game on Francisco Velez's second field goal, a 27-yarder that cut it to 14-6 with 12:11 to go.
The Tigers responded by handing off to Hill, who carried four times for 45 yards - including a gain of 26 yards to the Florida 19 - to set up Colby Delahoussaye's 31-yard field goal with 7:58 left.
Needing two scores, Florida started to gamble.
On fourth-and-5 from the Gators 30, punter Kyle Christy converted a fake, hitting Demarcus Robinson over the middle for a 15-yard gain. Murphy then converted a fourth-and-9 with a 15-yard pass to Ahmad Fulwood at the LSU 20.
That's when the Tigers' defense clamped down and sealed the game.
First came a sack on a blitz by cornerback Jalen Mills for a loss of 12 yards, which forced a desperate fourth-and-27. Another sack by linebacker Kendell Beckwith gave the ball back to the Tigers, who ran out the clock from there.
Florida entered the game giving up averages of only 217 yards and 12.2 points per game.
LSU gained 200 yards and scored 14 points in the first half.
After punting on their opening drive, the Tigers' next three series produced two touchdowns and could have resulted in a third score if Zach Mettenberger did not lose his handle on the ball without being hit for a lost fumble on the Florida 27.
Both scoring drives were helped by Florida penalties and gave LSU a 14-3 halftime lead.
Mettenberger finished with 152 yards through the air.