Stepan, who took a shot off his left ankle in Thursday's 5-3 win over Carolina, gave New York a 3-2 lead on a low slot rebound goal with 3:19 left in the game. Brad Richards scored an empty-netter in the final minute.
"I'm really happy how the guys handled themselves in between the second and third period," Rangers coach John Tortorella said. "I don't think there was any panic within them, and they just stayed with it. We have it rolling our way here. I thought we earned it. I don't think we went in the back door. I thought we grinded and stayed with it, and so we find a way to get a couple of points."
Lundqvist has started for the Rangers in their past 25 games, dating to Nov. 10, 2005, against the Lightning.
"It was tough going in after two (periods) and being down one, but the way we responded, it's just great to see and it's a very good sign," Lundqvist said. "We believe we can come back in games. A lot of it is confidence, too."
Tampa Bay went ahead 2-1 when Pyatt scored from the low left circle with 2:18 left in the second. Anisimov made it 2-2 at 6:16 of the third after a Tampa Bay defensive-zone turnover.
The Lightning had been 7-0-0 when leading after two periods.
"It's unfortunate," Lightning defenseman Marc-Andre Bergeron said. "We're not happy. Usually we're a strong team in the third. We have to turn the page."
Fedotenko tied it at 1 at 6:38 of the second with an in-close backhander off a pass from Richards. Both were key members of Tampa Bay's 2004 Stanley Cup championship team, which was coached by Tortorella.
Downie put the Lightning up 1-0 from the high slot 84 seconds into the game. Garon made a pad save midway through the first on Marian Gaborik's backhander during a breakaway.
Tampa Bay has held the lead after the first period just four times this season.
The contest was penalty-free until Lightning defenseman Pavel Kubina received an elbowing minor with 7:35 to go in the third. There were three penalties overall.
"It was a bit weird. ... It was a hard game, but guys kept it clean and kept their sticks down," Rangers captain Ryan Callahan said.
New York is 12-2-0 in its last 14 games. ... Tampa Bay C Steven Stamkos had an assist, extending his point streak (3 assists, 8 points) to six games. ... Stamkos and teammate Martin St. Louis both did not have a shot on goal.... Downie has three goals and 10 points in 10 games against the Rangers. ... Lightning C Nate Thompson stopped a personal 15-game point drought by assisting on Pyatt's goal. ... The game had a three-man officiating crew because linesman Pierre Champoux was ill.
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TAMPA, FL - DECEMBER 3: Ryan Malone #12 of the Tampa Bay Lightning smiles as he is greeted by fans before the...