The Hurricanes changed both story lines Tuesday night with a 3-1 victory against the Rangers.
"You have to wake up and just be confident in our game and our system and keep moving forward and looking ahead," Staal said. "The last couple games we've had haven't been a great result, but our effort has always been there. It's nice to get a good result."
Carolina had lost seven of eight to fall well behind in the Metropolitan Division race. The Hurricanes were outscored 30-16 in that stretch.
Elias Lindholm added an insurance goal for Carolina late in the third period. Cam Ward made 24 saves for his first win since Dec. 31.
"It has been a struggle for myself," Ward said. "I haven't had that much of an opportunity to get back in there.. When you don't play, you put so much emphasis on one game that it can get you thinking too much. Tonight, [I was] just be able to shut it off and have some fun."
"Not that I don't want to give credit to Carolina because they played a good game, but we [gave] away two points because we didn't work," Rangers coach Alain Vigneault said. "I have not said that very often about the group this year, but right from the start, our work ethic wasn't what it needs to be in this league to have any chance."
The Rangers had outscored the Hurricanes 40-19 in the teams' previous 10 meetings, including a 4-2 road victory on Friday. Before Tuesday, Carolina's last win against the Rangers was Jan. 20, 2011.
The Rangers, 8-4-1 in their past 13 games, remained one point ahead of Philadelphia for second place in the Metropolitan Division.
"I think we have to make a lot better decisions with the puck, especially in our own end," forward Derek Stepan said. "Offensively, we're a pretty skilled team, but to win hockey games, we have to make sure we do the dirty work in our own end and make good decisions. I felt like tonight we made it a little bit too easy for them to get in front and create chances."
Carolina took a 1-0 lead only 33 seconds into the second period.
Alexander Semin worked hard to control the puck in the offensive zone, eventually feeding it back to Andrej Sekera at the point. Sekera passed to Staal along the goal line, and Staal slid the puck under defenseman Anton Stralman to Tlusty for a one-timer that beat Lundqvist.
New York tied it at 1 only 3:49 later when Mats Zuccarello found Klein trailing the play on a rush. Klein was open in the slot, and his wrist shot went above Ward's left shoulder.
Carolina took a 2-1 lead with 1:42 left in the second. Staal outraced Stralman for the puck along the boards in the Rangers' zone and knocked it in front of Lundqvist. Tlusty gathered the puck to the right of Lundqvist and fed it back to a wide-open Staal before New York's defense could recover.
Lindholm finished the scoring with 5:29 remaining off a rebound of Jeff Skinner's original shot.
"I think we played a really strong 60 minutes of hockey," Carolina coach Kirk Muller said. "There was still a lot of fighting with these guys. ... Hopefully tonight is that big win that we build on."
Carolina's Jay Harrison played in his 300th NHL game. ... The Hurricanes' John-Michael Liles missed his second successive game with an upper-body injury. ... Stepan saw a six-game point streak snapped. Stepan had one goal and eight assists in that span.