Chris Higgins, David Booth and Stephen Weiss scored for the Panthers, who had dropped three of four.
Martin Biron stopped 33-of-35 shots in the loss for the Rangers, who have dropped four of their last six.
After the first period went scoreless, the Panthers took a 1-0 lead at the 11:32 mark of the second with a power-play goal. After Mike Santorelli shot from the left circle, Booth cleaned up the rebound in front for his 10th goal of the season.
Vokoun, who stopped seven shots in the first frame, made 14 saves in the second to keep the Rangers off the board.
Florida appeared to get some insurance 3 1/2 minutes into the third when Cory Stillman scored from in front, but the video review showed he kicked the puck in and the goal was nullified.
However, the Panthers did get their second goal about five minutes later. Higgins skated down the left wing, dragged the puck back to get around a defender and chipped the puck into the left corner from the slot.
The Rangers got a power play with 3:26 to play and later pulled Biron for a 6-on-4, but were unable to take advantage. Weiss scored a shorthanded empty- netter to seal the win.
Florida plays at Carolina on Monday…New York returns home to face Carolina on Wednesday…New York beat Florida, 3-0, on November 26 and had won four straight in the series…Vokoun has 43 career shutouts.