The Columbus Blue Jackets, meanwhile, have reached a tipping point.
Hagelin scored two goals - one thanks to an opposing player - and Talbot made 32 saves to lead the Rangers past the Blue Jackets 4-2 on Thursday night.
After Columbus' fifth loss in a row, forward Brandon Dubinsky and coach Todd Richards each said they were humiliated by the team's lack of effort.
''There's really nothing left to say,'' Dubinsky said. ''It's flat-out embarrassing for us, our fans, for the organization. Thank God for (goalie Sergei Bobrovsky). It could have been 10-1 before we had an opportunity to come (out for) the third period.''
The Blue Jackets closed last season on a 19-5-5 tear - the second-best record down the stretch in the entire NHL. But they are 5-10-0 this season and wallowing near the basement of the Eastern Conference in their first year since making the move over from the West.
''That was embarrassing hockey tonight,'' Richards said. ''That's losing hockey, the way we played. We got exactly what we deserved. It could have been 7-1 going into the third period. Our goalie was great. There was not enough battle, not enough compete. Simple as that. Really disappointed in our group.''
In the other dressing room, the mood was celebratory. The Rangers have won five of their last six to climb in the standings and get back to 8-8-0 on the season.
''We want to play better than we have,'' Hagelin said. ''We know we should be .500 at least. It's good to be there; now we've just got to start climbing.''
Coach Alain Vigneault lauded his team's effort during a busy time.
''For us, it was back-to-back nights, four (games) in six nights, three in four, and the end of a pretty long stretch here where we played nine games in 15 nights,'' Vigneault said. ''We did what we had to do to win the game. We talked about making it a greasy third period. And we did that for the most part.''
Rangers captain Ryan Callahan and defenseman Ryan McDonagh each added a goal and an assist.
There were plenty of familiar faces on both sides - four players on each team used to play for the other one.
Talbot, giving Henrik Lundqvist a night off, was the third straight backup goalie to face the Blue Jackets. All three have won, combining to give up just three goals.
Talbot made several solid saves in the scoreless third period, stymieing former Ranger Artem Anisimov on a backhander in the crease on a power play in the final minutes.
''He played great again,'' defenseman Marc Staal said of Talbot. ''He made very timely saves when we need them. He's been rock solid since his first start. We have all the confidence in the world in him.''
A wild second period saw the Rangers score two of three goals - one when a Blue Jackets player put the puck in his own net.
At the 4:17 mark, with the Rangers on a power play, McDonagh's hard shot from the point was redirected twice. First it glanced off Mats Zuccarello before it ricocheted into the net off a redirect by Callahan.
New York made it 3-1 at 12:44 on a fluke. Columbus forward Mark Letestu tried to clear the puck from the left corner but instead he lost control of it and pushed it past Bobrovsky from a hard angle. The goal was awarded to Hagelin.
''We came out hard,'' Hagelin said. ''We played OK in the first couple of minutes, then we gave them some chances. In the second, we did a good job. They were in the (penalty) box a lot and our power play is looking pretty good right now.''
Ex-Ranger Fedor Tyutin scored his first of the season and rookie Ryan Murray also had a goal for the Blue Jackets, who lost despite several highlight-reel stops among the 30 saves by Bobrovsky.
He stopped Brian Boyle on a breakaway. Then, in the opening 90 seconds of the second period, Bobrovsky made three big saves - one on Brad Richards, who came in 1-on-1 after a turnover - and then two against Zuccarello on one rush. Bobrovsky also was sprawled on his stomach when he gloved a backhander by Derek Stepan.
Dubinsky could not shake his anger about the lack of effort.
''We need to take a hard look in the mirror, as an individual and as a team,'' he said. ''Then we need to find a way to correct it. It should be the easiest thing to correct. I mean, really, it's not a systematic thing or a teaching thing. We're all in the NHL now. We should be here because of hard work and effort and second and third effort. So we know how to do it. We just have to go out and do it.''
NOTES: Before the season, the game was expected to mark the return of former Blue Jackets captain Rick Nash, but he's missed the last 13 games with a concussion. ... Hagelin has four goals this season and points in his last four games (four goals, two assists). ... The Blue Jackets haven't led since early in the second period against Anaheim on Oct. 27 - almost 280 minutes of ice time.
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