Naslund scored twice and had one of two New York goals in a shootout to lead the Rangers past the Lightning, 3-2 on Wednesday night.
"We know that this building is a tough building to play in, and they're a desperate team," Naslund said. "We had to work hard to get the win, but it was nice to get it."
Nikolai Zherdev had two assists, and also scored in the shootout. Henrik Lundqvist stopped 27 shots in regulation and also turned aside both Tampa Bay shots during the shootout.
"We played hard, stayed intense," Rangers coach Tom Renney said. "That's a sign of a mature team."
Lundqvist is 10-4-2 -- allowing six goals in four victories this season -- against Tampa Bay. The Rangers swept the four-game season series -- that included two games in the Czech Republic -- with the Lightning.
"I guess we like the challenge to play this team," Lundqvist said. "We had a good start of the year in Prague when we played this team."
New York has won five of its last seven games.
"We talked about trying to get some momentum going here and put a string of wins together," Naslund said.
Mark Recchi pulled the Lightning even at 2 when he scored with 49.6 seconds left in the third. The goal gave him 1,395 points, moving him past Luc Robitaille into 19th place on the NHL career list.
Ryan Malone also scored for the Lightning, who have lost nine of 11. Four of the losses have come in overtime or a shootout.
"It's disappointing, obviously, not getting the two points, but it's not a lack of effort," Tampa Bay right wing Martin St. Louis said. "If we play like that and battle like that game in and game out, I like our chances of coming out on top."
Naslund put the Rangers ahead 1-0 at 2:40 of the second when he picked up a rebound and then made a couple nifty moves to beat Lightning goalie Mike Smith.
Malone tied it at 1 on a rebound power-play goal 1:29 later. The Rangers entered with the NHL's best road penalty-killing unit, allowing just three power-play goals in 45 short-handed situations before Malone's goal.
New York went back up 2-1 on Naslund's power-play goal with 2:03 left in the second, redirecting Michal Rozsival's shot while positioned in the slot.
Tampa Bay center Steven Stamkos, taken first overall in this year's draft, has gone 12 games since scoring his only two goals this season in a game against Buffalo on Oct. 30. He did have a spirited fight late in the first period with Zherdev.
Smith made 33 saves. ... Lightning LW Matt Pettinger didn't play due to a right knee injury. ... Zherdev has six assists in his last three games. ... Tampa Bay C Vincent Lecavalier had an assist to extend his point streak to five games. He has three assists and six points over the stretch. ... Naslund has two goals and four points during a four-game point streak. ... Tampa Bay reassigned D Jamie Heward to Norfolk of the AHL. ... Rozsival had two assists.