Malone beat Henrik Lundqvist from the slot as his game-winner stopped a personal 10-game goal drought.
Brandon Dubinsky got the Rangers even at 3 from the left circle with 3:27 left in the third.
Steven Stamkos scored his league-leading 45th goal from slot at 10:17 of the third to give the Lightning a 3-2 lead.
Tom Pyatt and Teddy Purcell also scored for the Lightning, who moved within four points of eighth-place Winnipeg in the East. Purcell added two assists.
Artem Anisimov and Marian Gaborik had other Rangers' goals. New York dropped to 29-1-3 when scoring the game's first goal.
Purcell tied it at 2 from just outside the crease off a nifty pass from Martin St. Louis at 3:37 of the third. Purcell has five goals and 17 points during a career-high eight-game point streak.
The Lightning got within 2-1 when Lundqvist had the puck go off the tip of his glove before Pyatt poked it home 7:09 into the second.
Tampa Bay is 7-25-3 when behind entering the third.
Anisimov put the Rangers up 1-0 from the left circle at 10:09 of the first. The Lightning outshot New York 9-1 before Anisimov's goal.
Gaborik made it 2-0 on his 31st goal this season, coming during a 5-on-3 power play at 2:43 of the second. The goal came on the Rangers' fifth shot on Mathieu Garon, who finished with 16 saves. Lundqvist stopped 27 shots.
Rangers captain Ryan Callahan missed his second consecutive game due a bruised right foot. New York defenseman Michael Del Zotto sat out because of a hip injury.
Notes: New York D Jeff Woywitka was in the lineup for the first time since Dec. 30. He had been scratched the previous seven games after completing a minor league conditioning assignment following a foot injury with Connecticut of the AHL. ... Tampa Bay RW Ryan Shannon played after missing three games with an undisclosed upper body injury. ... The Lightning signed F Danick Gauthier, currently playing with Saint John of the QMJHL, to a three-year contract.