The Rangers began the night tied with Winnipeg for the eighth playoff position in the Eastern Conference, but had a game in hand against the Jets.
Mats Zuccarello and Derick Brassard produced two goals each while Lundqvist stopped 34-of-35 shots. Florida, the team with the worst record in the NHL, lost its fourth in a row.
Brassard opened the scoring on the power play 3:05 into the game, helping stake the Rangers to a 2-1 lead after one period.
Zuccarello scored late in the second period to give New York some breathing room and the Rangers then came up with three goals in the game's final 4:41 -- those tallies coming from Zuccarello, Brassard and Brad Richards.
Scott Clemmensen made 24 saves in the losing effort.