Florida's Craig Anderson made 40 saves and allowed only a first-period goal to Markus Naslund.
The Rangers remain winless under Coach John Tortorella, who replaced Tom Renney Monday. New York last lost four straight and 12 out of 14.
Henrik Lundqvist took a shutout into the third period, but the game changed just past the midway point of the stanza when Booth fired a backhander from the right circle that got between Lundqvist and the right post with 8:10 remaining in the contest. Horton then deflected the puck off the goaltender from behind the net for the game-winner.
Florida won the season series 3-1.