Horton picked up a loose puck in front of the crease and poked the puck over the pads of Johan Holmqvist.
Ruslan Salei, Stephen Weiss, Bryan Allen and Ville Peltonen also scored for Florida, and Ed Belfour had 16 saves.
Martin St. Louis scored two goals for Tampa Bay. Eric Perrin and Dan Boyle also scored, and Holmqvist stopped 25 shots as the Lightning snapped a three-game winning streak.
Florida tied the score at 4 during a power play at 11:28 of the third. Olli Jokinen sent a pass across the crease and Peltonen poked in the puck just inside the right post.
Florida tied the score at 3 on Allen's goal. His shot from the right circle beat Holmqvist at 6:48 of the second.
The Lightning reclaimed the lead about five minutes later during a power play when Boyle's shot deflected off a defender and went into the net.
Trailing 2-0, the Lightning scored three goals on seven shots in the first period, two of them by St. Louis.
St. Louis' one-timer off a pass from Vaclav Prospal pulled Tampa Bay to 2-1 at 6:09. The Lightning tied the score on Perrin's goal on a backhander at 11:03.
Tampa Bay went ahead at 16:28 as St. Louis took a pass from Boyle in front of the crease and slipped the puck past Belfour.
Florida took a 1-0 lead on Salei's power-play goal on a shot from the top of the right circle 1:47 into the game. Weiss's goal at 4:02 made it 2-0.
Notes: Tampa Bay's Vincent Lecavalier has 18 goals and 21 assists in his last 20 games. ... Florida's Rostislav Olesz, out with a shoulder injury, returned to the ice tonight for the first time since Feb.8.