"Sometimes it's a good thing to get a lot of work," Lundqvist said. "There's been a lot of games where I've been waiting for shots, and then there's been some odd-man rushes or breakaways, and it's been hard to really get the game going.
"A game like this definitely helps you to work on your positioning and a lot of different things, so I'm pleased with the win and the way I played."
Lundqvist watched from the bench as backup Cam Talbot started the previous three games, winning two, after Lundqvist struggled through a 1-4-2 stretch.
"He played a real strong game, gave us a chance to win, especially in the third when they had a real strong push and they were tough to handle," Rangers coach Alain Vigneault said. "He had some huge saves to make, and he did."
"They earned that victory," Lightning captain Martin St. Louis said. "We got what we deserved."
The Rangers went up 4-2 on second-period, power-play goals by Kreider and Pouliot.
Kreider beat Anders Lindback with a backhander at 4:35, and Pouliot extended his point streak to seven games with an in-close redirection 3:16 later.
Tampa Bay pulled within 4-3 on Filppula's tip-in 8:14 into the third. It was one of 16 shots the Lightning had on Lundqvist during the period.
"Hank was our best player," Zuccarello said. "He played really well for us. They had numerous chances, and we were a little bit nervous there in the third period."
After Johnson tied it with a power-play goal at 10:41 of the first, Palat scored a rebound goal from the left circle to make it 2-1 with 3:55 left in the period.
Zuccarello got the Rangers even at 2 during a power play when his pass into the low slot deflected off Gudas into the net at 18:25. The center assisted on goals by Kreider and Pouliot.
"I don't think I've seen us mismanage the puck more," Tampa Bay coach Jon Cooper said. "That was painful to watch, to be honest."
NOTES: Lightning star Steven Stamkos, out since breaking his right leg on Nov. 11, did a series of agility drills during a 30 minute on-ice workout. The center, who hopes to return in February, resumed skating 2½ weeks ago. ... Rangers RW Ryan Callahan (sprained knee) had a limited workout, wearing a no-contact jersey, during the team's morning skate. ... Tampa Bay D Eric Brewer (upper body), Sami Salo (upper body) and LW Ryan Malone (broken ankle) could return during a four-game trip that starts Wednesday at Vancouver. ... New York D Marc Staal (concussion) and D Anton Stralman (left hand and wrist) practiced. ... Tampa Bay D Dmitry Korobov assisted on Filppula's goal for his first NHL point. ... Rangers D Conor Allen played nearly 16 minutes in his NHL debut.