The victory, before a crowd of 73,021 at Florida Field, stopped a two-game losing streak and might send the Gators, 6-4 overall and 3-3 in the Southeastern Conference, to the Aloha Bowl in Honolulu on Christmas Day. Bowl bids will be extended next Saturday.
Kentucky fell to 5-5 and 1-4.
Bell, who finished with 12 completions in 20 attempts, became the leading career touchdown passer in the SEC with his 39-yard pass to Simmons.
It was the 55th touchdown pass of Bell's career, moving him ahead of Florida's John Reaves on the all-time SEC list. Bell has thrown for 7,471 yards in four years, 78 shy of Reaves' conference mark of 7,549 yards.
Florida's Emmitt Smith, the SEC's leading rusher with 1,241 yards, gained 112 yards in 24 carries, his seventh 100-yard game of the season but his first in three weeks.
LSU (8-1-1, 5-1) scored twice in the first 4 1/2 minutes on a 7-yard run by Martin and a 13-yard pass from Tom Hodson to Wendell Davis, who had 4 catches for 62 yards to set an SEC record for career receiving yardage of 2,626 yards, breaking the mark of 2,625 set by LSU's Eric Martin from 1981 to 1984.
After Mississippi State (3-7, 0-5) tied the score, 14-14, Hodson completed a 32-yard touchdown pass to Martin, David Browndyke kicked field goals of 49 and 26 yards and Harvey Williams ran 6 yards for a touchdown to complete LSU's scoring.
Keith Davis was the Vols' top ground gainer with 100 yards in 13 carries. Cobb added 81 yards in 13 carries and scored on runs of 9, 1 and 13 yards.
Cobb's three touchdowns put him within six points of tying the SEC record of 120 points in one season shared by Herschel Walker of Georgia (1981) and Tommy Durrance of Florida (1969). Cobb has two games remaining.