The Rangers are looking for a breakout from forwards Rick Nash and Brad Richards.
After Holtby denied Brad Richards, Backstrom beat Lundqvist to decide the contest in the fourth round.
Brad Richards, who also assisted on Gaborik's winner, got the Rangers within 2-1 in the second.
Brad Richards scored once over the first 10 games before Tortorella benched him for the final two.
New York's Brad Richards found Marian Gaborik with just over five minutes left in the third overtime.
The Sabres forward shoved Rangers center Brad Richards from behind and into the boards on Sunday night.
New York struggled to score in the postseason, and Nash and Brad Richards were among the biggest offenders.
Rangers F Brad Richards, the 2004 Conn Smythe Trophy winner, was a scratch for the second straight game.
Sabres RW Patrick Kaleta served the second game in his 5-game suspension for boarding Rangers C Brad Richards.
Marchand scored for Boston to tie it, and Brad Richards missed for New York before Krejci went wide.
The last came with 1:54 remaining after Ovechkin was high-sticked by Brad Richards.
New York's first goal came on a power play after three Hurricanes followed Brad Richards to the goal line.
"It's always nice to beat them, " said Brad Richards, who had two assists.
The Rangers started the season with a high-powered top line of Marian Gaborik, Brad Richards and new acquisition Rick Nash.
Lundqvist had to hold off the surging Capitals in the closing minutes after Brad Richards was whistled for high-sticking Alex Ovechkin.
Brad Richards and Chris Kreider also scored for the Rangers, who have won 11 of the last 12 meetings with Philadelphia.
While Pyatt has three goals already, the Rangers need more from the top line of Gaborik, Brad Richards and Rick Nash.
That's one thing about Brad Richards, I think he understands that stuff.
"I don't want to talk about penalties, " Rangers center Brad Richards said.
Brad Richards and Hagelin staked the Rangers to a 2-0 lead, but goals by Mathieu Perreault and Troy Brouwer tied it for Washington.
He benched veteran forward Brad Richards for the final two games of the Boston series (though Sather said Wednesday that was an "organizational decision").
Brad Richards tied it for the Rangers with 2:57 left in regulation after New York blew an early 2-0 lead and fell behind already-eliminated Carolina.
The Rangers have been looking for depth at forward to complement their top line of Rick Nash, Brad Richards and former Wild star Marian Gaborik.
Dubinsky spent much of the early part of the season playing with two of the Rangers' most skilled offensive players, center Brad Richards and right wing Ryan Callahan.
Brassard spun in the left circle and backhanded a pass back to Brad Richards at the point for a drive that hit Boyle in front and caromed in.
It would have seemed impossible that New York could have won even one series without a goal from Nash and only one each from captain Ryan Callahan and Brad Richards.
New York regrouped and worked the puck back into the Pittsburgh end, but Taylor Pyatt accidentally collided with teammate Brad Richards behind the Penguins' net and the puck was cleared.
First things first: Before the team's morning skate, coach John Tortorella called Brad Richards, the team's highest-paid and most accomplished forward, to tell him that he would bench him for Game 4.
"Where we operate now, people aren't afraid, " said Brad Richards, executive vice president of the Illinois Oil and Gas Association, who says fracking is safe and concerns about its environmental impact overblown.
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