"With where we're at in the standings, teams have a chip on their shoulder when they come play us, and we've got to be prepared for that," Dubinsky said.
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. New York (26-0-3) still hasn't lost when ahead after the second.
"I thought we were late in a lot of plays," Rangers coach John Tortorella said. "We really struggled with our battles in the corners. The team that played the best won, but I'm still happy about us bouncing back and finding a way to get a point anyway."
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.
"It could have been very discouraging, but it wasn't," Boucher said. "The first period, we're all over them. Our players have really developed this mental toughness to fight through. We're getting rewarded for not quitting."
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.
"I felt like they made it tough for us all night," Lundqvist said.
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.
All four games in the season series -- which was split -- were won by the team trailing entering the third. ... 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.
Copyright by STATS LLC and The Associated Press
Arena: Amalie Arena Location: Tampa, Florida
Referees: Mike Leggo, Brian Pochmara Linesmen: Ryan Galloway, Matt MacPherson
Attendance: 19,204 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Artem Anisimov (13)
Assist: Ryan McDonagh
Marian Gaborik (31)
(Power Play) Assists: Derek Stepan, Brad Richards
Tom Pyatt (7)
Assists: Brett Connolly, Brian Lee
Teddy Purcell (18)
Assists: Martin St. Louis, Steven Stamkos
Steven Stamkos (45)
Assists: Brian Lee, Teddy Purcell
Brandon Dubinsky (7)
Assists: Marian Gaborik, Anton Stralman
Ryan Malone (11)
Assists: Teddy Purcell, Eric Brewer