"We worked so hard, so this is a big one for us," said Lundqvist, who had 35 saves. "Playing such a good team and the position we're in, we're desperate for points and wins, so just a great feeling the way we played and got rewarded in the end with that big goal."
The Rangers (22-20-3), who began the day in 10th place in the Eastern Conference, improved to 6-2-1 in their past nine games. They were coming off a 4-3 shootout loss at home against Columbus.
Asked whether the victory over Chicago could be a tipping point for New York, coach Alain Vigneault said: "All I know is beating the Stanley Cup champions in this building is not an easy task."
Jonathan Toews and Brandon Bollig scored in the second period for Chicago (29-8-9), which had recorded at least one point in a season-high 10 games. Coupled with Sunday's shootout loss against San Jose, the Blackhawks lost consecutive home games for the second time this season.
It was Chicago's first regulation loss since it was blown out at Toronto, falling 7-3 on Dec. 14.
"We've got too many guys right now that aren't contributing to that level we saw most of the season," Blackhawks coach Joel Quenneville said.
Marc Staal started the winning sequence with a long slap shot that was stopped by Corey Crawford, who also got in front of Hagelin's first rebound attempt. But Hagelin stayed with the play and flipped the puck into the open right side with 5:57 left.
It was Hagelin's fourth winning goal of the season, tops on the team. He also is tied for the team lead with 11 goals overall.
"Lately, we have a lot of confidence and try not to get too frustrated," Hagelin said. "Some games the puck goes in and other days it doesn't. But I think when you're creating chances you stay positive."
The Rangers and Blackhawks took turns controlling the action in the first two periods.
The first belonged to New York, which made the most of a disjointed start for Chicago. Richards scored on a wrist shot at 5:06, and Zuccarello made it 2-0 when he skated behind the net for a wraparound that banked off the paddle of Crawford's stick for a power-play score at 9:29.
Lundqvist had the secondary assist on Zuccarello's 11th goal. It was Lundqvist's second assist of the season and 14th of his career.
"Especially there in the first we were sloppy," Blackhawks defenseman Duncan Keith said. "We got better as the game went along, but unfortunately, they were able to get one late."
Chicago bounced back in the second, using a power play to get back in the game. With Derick Brassard in the box for interference, Toews beat a screened Lundqvist high on the stick side for a rebound goal at 6:17.
It was Toews' 16th of the season and first since Chicago's captain scored twice during a 7-2 victory over Colorado on Dec. 27.
The Blackhawks struck again 1:48 after Toews' goal. Bollig skated alone down the left side and tied it at 2 with a well-placed wrist shot into the lower left side of the net. It was Bollig's fourth goal of the season.
Crawford settled down after the uneven start and finished with 29 saves. He made a nice glove save on Rick Nash on a semi-breakaway with 2:05 left in the second, keeping the game tied at 2. He also used his right pad to deny Brassard early in the third.
The 26-year-old Zuccarello is tied with Richards, Hagelin and Chris Kreider for the team lead in goals. Zuccarello's previous career high was six goals when he was a rookie with New York in the 2010-11 season. ... The Blackhawks recognized their 10 Olympians on the center-ice video board during a break in the first period. ... New York C J.T. Miller and D Justin Falk were scratched. ... Defensemen Michael Kostka and Sheldon Brookbank were scratched for the Blackhawks.
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