The Rangers moved ahead of Atlanta and into ninth place in the Eastern Conference, two points behind Philadelphia and Boston at the postseason cutoff. New York has five games remaining, the same amount as Boston and one more than Philadelphia.
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"It's tough when you have to scoreboard watch a little," forward Brandon Dubinsky said. "But you play for the pressure and you play for the chance to get an opportunity to win the Cup."
Three of the Rangers' five goals were put in the net by Lightning players.
"Unfortunately, it happens," Lightning right winger Mark Parrish said.
Prust scored 3:09 in, Marc Staal doubled the lead 25 seconds later, Vaclav Prospal added a goal, and Dubinsky pushed the lead to 4-0 with a power-play tally before 15 minutes had elapsed. Aaron Voros finished the scoring late in the game.
The Rangers have gone 4-0-1 in their past five to get back into the thick of the playoff race.
"We're happy to win, but we're still in a tough spot, and it's important we stay focused," Lundqvist said. "Nobody's real excited, so we just break it down now to every game ... and try to play our best right down the stretch."
Prust started the onslaught with his third goal of the season, beating goalie Mike Smith between the pads. Staal made it 2-0 with his seventh, scoring at 3:34.
Prospal added his 19th goal when his pass through the crease deflected in off the skate of Lightning defenseman Vladimir Mihalik. The Rangers benefited from another fortunate bounce when Dubinsky's shot deflected through Smith and caromed in off Kurtis Foster's skate.
"It's hard to gauge a game when it's boom boom boom and there's three goals right away," Lightning coach Rick Tocchet said. "We're not a team that can recover from soft goals. When it's boom boom boom like that there's not much you can do."
Voros goal was aided by Lightning goalie Antero Niittymaki trying to clear a loose puck.
"We got fortunate because I think three went off their skates," Rangers coach John Tortorella said, "but you're getting the puck to the net and good things happen."
Smith, who made just three saves on seven shots, was replaced at the start of the second period by Niittymaki.
The Lightning had chances to cut into the deficit when they had a long 5-on-3 advantage early in the second. However, the Rangers limited Tampa Bay to one shot and killed the penalties to Jody Shelley (holding) and Dubinsky (delay of game).
"What if they score two on the 5-on-3?" Tortorella asked. "I thought we did a great job taking away some of their options that they wanted."
The Lightning were 0-for-4 overall on power plays. Niittymaki made 14 saves in his two periods of action.
Despite a 2-0 win at Pittsburgh on Wednesday, the Lightning are on the verge of being eliminated from the playoff race.
"I haven't thought too much about that," Tocchet said. "We've still got games to play."
There was a brief stoppage 14:24 in after Lightning RW Steve Downie was injured. Downie and Rangers D Daniel Girardi crashed into the boards behind the New York net, and Girardi's stick was driven into Downie's midsection during the collision. He stayed down for several minutes, but was able to skate off -- declining to get onto a stretcher that was brought on the ice. Downie returned in the third period after tests showed there was no damage to his spleen and no signs of internal bleeding. "It was scary when I couldn't breathe there for about two minutes," Downie said. "After the hospital, I wanted to go back in the game." ... Lightning D David Hale missed his fourth straight game because of a lower body injury.
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Arena: Tampa Bay Times Forum Location: Tampa, Florida
Referees: Dan O'Rourke, Dan O'Halloran Linesmen: Scott Driscoll, Thor Nelson
Attendance: 17,909 (90.6% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Brandon Prust (3)
Assist: Artem Anisimov
Marc Staal (7)
Assist: Marian Gaborik
Vinny Prospal (19)
Brandon Dubinsky (19)
(Power Play) Assists: Dan Girardi, Anders Eriksson