Stepan started the four-goal barrage when he stole the puck at center ice, skated all the way in on Panthers goalie Jose Theodore and beat him between the pads with a forehand shot for an unassisted tally 5:45 into the decisive frame.
Artem Anisimov added a goal and an assist. Brad Richards also found the net for the Rangers, who won for the 14th time in 18 games.
Henrik Lundqvist stopped 20-of-21 shots to earn the victory.
Theodore was pulled after two periods for Florida, having yielded all six goals on 22 shots. Scott Clemmensen replaced him and turned aside all 11 shots he saw the rest of the way.
Erik Gudbranson, Florida's third-overall pick in the 2010 NHL draft, netted his first career goal for the Panthers' only score.