Florida has won back-to-back games for the first time this season.
The Panthers took a 2-0 lead into the final period, but Marian Gaborik gave the Rangers hope by scoring on a backhander with 3:48 to go.
Markstrom was perfect the rest of the way and Tomas Kopecky clinched the victory by scoring shorthanded into an empty net with 46 seconds remaining. Markstrom made 17 saves in the third period.
Florida ended a six-game losing streak on Tuesday with a 4-1 victory over Carolina. The Panthers have now won two in a row for the first time since March of last season.
The Rangers outshot Florida 45-23, but had a two-game win streak come to an end. Henrik Lundqvist stopped 21 shots for New York.