Hagelin scored the game-winning goal late in the second period and added a third-period insurance goal to help the Rangers break a two-game losing streak and finish their three-game road trip on a winning note.
Hagelin, playing on the left side with with center Brad Richards and right wing Benoit Pouliot, helped the Rangers overcome two Jets goals 53 seconds apart in the first period. He erased a one-goal deficit and put the visitors on top with his second goal of the game with 7.8 seconds left in the second period.
The win moved the Rangers (36-28-4) into second place in the Metropolitan Division, two points ahead of the Columbus Blue Jackets.
The loss pushed the Jets' (30-29-9) losing streak to six games (0-3-3). They are six points behind the Dallas Stars for the Western Conference's second wild-card spot in the Stanley Cup Playoffs.
Henrik Lundqvist allowed two goals on the first five shots he faced, then held the Jets scoreless the rest of the way. He finished with 30 saves to tie Mike Richter for the franchise record with 301 victories.
"Our goaltender had to make some good saves, and he did at the right time," Rangers coach Alain Vigneault said.
Dustin Byfuglien and Andrew Ladd scored for the Jets. Ondrej Pavelec made his seventh start in the past eight games, but departed the game with an undisclosed injury after the first period having allowed two goals on eight shots. Al Montoya took over for the Jets and stopped 13 shots in relief. Pavelec will be evaluated further on Saturday.
Martin St. Louis, whom the Rangers acquired in a trade from the Tampa Bay Lightning on March 5, helped set up the winning goal. St. Louis beat defenseman Jacob Trouba to a puck dumped behind the Winnipeg net and backhanded a pass into the slot, where Hagelin lifted his second goal of the game over Montoya.
Hagelin has has 16 goals this season but had scored just once in his past 13 games and twice in 22 games before his outburst against the Jets. The 25-year-old left wing has three multigoal games this season. With the Jets on the power play late in the third period, Hagelin also made a key block on Trouba's point-blank shot.
"We haven't played the way we wanted," Hagelin said. "To get two points was huge. We move on from this and gain some confidence. We've got to play even better than this if we want to make the playoffs."
Hagelin opened the scoring 1:15 into the first period. Klein let go a right-point shot that Hagelin tipped, catching Pavelec leaning the wrong way.
However, the Jets responded with two quick goals. Byfuglien scored 1:18 after Hagelin's goal, using his long reach to swat Blake Wheeler's centering pass out of the air and past Lundqvist at 2:33 for his 17th goal. Ladd celebrated his 600th NHL game with a rising wrist shot that climbed over Lundqvist's right shoulder at 3:26 for his 19th goal.
"I thought we had momentum after 2-1 and playing well," Ladd said. "We needed a little more from our power play (0-for-4 against the Rangers) to generate some momentum, and we didn't get that."
Kreider tied the game at 11:28 by taking Derek Stepan's long outlet pass, outracing Winnipeg defenseman Zach Bogosian and snapping his 17th goal past Pavelec to the short side. Kreider has three goals in his past four games. Hagelin followed with the go-ahead goal late in the second and added the insurance goal at 8:50 of the third period to complete his hat trick.
"I thought we responded to the first (Rangers goal) very well, and I liked our game straight through to the tying goal," Jets coach Paul Maurice said. "Our power play struggled in the second period. And then clearly the 3-2 goal changed how we moved the puck and how we moved some things around. It was tough."
Lundqvist settled in and carried the Rangers in stopping the final 27 shots he saw.
"After that second goal, it's about how you respond," Lundqvist said. "We just did in the right way. We didn't let it get to us. We kept working really hard."
"It was just a mindset," Lundqvist added. "After the second goal, you're upset and you just try to push yourself to be better. I'm happy with the way I responded, and I'm really happy with the way the team responded. It was such a huge game for us, and we needed the points big-time. I'm happy."
"The past four or five games, I feel like I'm playing the way I want to play," said Lundqvist, who is 3-1-1 in his past five games. "A lot of it is just being focused and making decisions, [fewer] technical mistakes when you're focused in the right place. It's fun to play right now. [These are] important games and big points ... that we're trying to get."
Lundqvist can pass Richter and establish a franchise record for wins Sunday against the San Jose Sharks at Madison Square Garden.
"It's a huge honor to be up there with [Richter]," Lundqvist said. "He has meant so much to this organization, and it's kind of surreal to see yourself up there with him. I'm extremely proud to be up there with him.
"It also means that I have been here for a while now, and I've been lucky to play with a lot of great players and coaches who helped me get there. I'm really excited and proud of it. I hope I have a lot more to give."
The Jets host the Stars on Sunday in what might be their final opportunity to push themselves back into contention. They admit that their lack of success is testing them.
"It's getting harder right now," center Bryan Little said. "We're really fighting to win, and [wins are] not coming easily by any means. The more it drags on, the [harder] it is to put it behind you and focus on the next [game]."