He also assisted on Rick Nash's first-period goal that put New York in front 1-0.
Lundqvist turned aside every Stars shot in the first and stopped 35 of 36 through 40 minutes to keep the Rangers in a 1-all tie.
"The way the game was played, I had to be aggressive," Lundqvist said. "Especially in the first, it felt like the puck was all over the place, and they were putting a lot of shots on net and rebounds.
"It felt good to get a period like that, to really work hard."
Chris Kreider and John Moore scored 37 seconds apart in the first 1:55 of the third period to give New York a 3-1 lead.
Rangers coach Alain Vigneault appreciated the effort of his star goalie, especially his contribution to the offense.
"Henrik made an unreal pass so that we had that quick breakout, that quick strike (by Nash)," Vigneault said. "After that, Henrik put on a display in the first period."
The third-period goals took some pressure off Lundqvist, who entered the game with a 7-9 record despite a 2.38 goals-against average.
"We came out in the third and just made up our mind we need this game," Lundqvist said. "That was a great feeling, to see we scored two quick ones there."
Alex Chiasson brought Dallas back within a goal by scoring at 8:27 of the third.
It just wasn't enough.
"We can't be happy with the way (the first period) came out because it was 1-0," Stars coach Lindy Ruff said. "You have to give Lundqvist a lot of credit.
"The one goal they scored came on a power play when we were dumping it up ice, and we get caught on a breakaway. You can't do that."
Just 12 seconds after Chiasson's goal, Stars goalie Kari Lehtonen stopped Nash on a penalty shot.
Nash had scored New York's first goal at 6:27 of the first period. It was his first goal this season, in his second game back after missing 17 games because of a concussion.
"I was hoping he thought I was going to do the same move that I scored on, and then bring it right back and tuck it in," Nash said. "He played it well."
Lehtonen knew Nash has several tricks in his scoring arsenal.
"I needed to make that save against Nash to keep it a one-goal game," Lehtonen said. "He has three or four different moves. He scored the first one on a breakaway when I thought he was going to do something else.
"On the second one, I just had to be patient. My long legs helped me there. I was able to reach out and get that one."
Dallas' best chance to tie the game came with three minutes remaining.
Jamie Benn's shot from in front hit Lundqvist, who wrapped himself around the puck to prevent a rebound.
"The biggest save of the night was Lundqvist's on Benn's play," Ruff said.
When Dallas tied it 1-all on Stephane Robidas' goal at 8:46 of the second period, it was the Stars' first power-play goal in eight home games this season. They had been unsuccessful in their first 26 opportunities.
The Rangers, who started a five-game road trip, had scored only two goals -- both on the power play -- in their three previous games, in which they went 1-2.
Nash's go-ahead goal came on New York's first power play of the night. He skated in, put the puck on his forehand and pushed it in the net to the right of Lehtonen.
"When you're struggling at scoring, you've got to look to your special teams for a boost, and tonight we got it," Nash said.
Dallas had two first-period power plays but failed to score even though it put six shots on Lundqvist.
The Stars broke through with Robidas' third goal. He took a cross-ice pass from Sergei Gonchar at the left point and blasted a slap shot that deflected off a defender and past Lundqvist.
New York had an apparent goal disallowed about five minutes later. From a scramble in front, the puck went into the upper right corner of the net. On review, it was determined that Rangers center Derick Brassard had batted the puck across the goal line.
During the period, Lundqvist exceeded his previous season high of 31 saves.
The Rangers came out quickly in the third and recorded the first four shots. On the third drive, Kreider broke the tie. Their next shot was the goal by Moore.
Lundqvist then did the rest to protect the lead,
"You can talk about him every single night," Nash said. "He was the best player on the ice and he was the difference."
Dallas went 1-for-5 on the power play. In the Stars' past 10 games overall, they are 3-for-35. ... Nash is one of three current players, with the Islanders' Thomas Vanek and the Capitals' Alex Ovechkin, who entered the season with eight consecutive 20-goal seasons. ... Lundqvist's career high for saves is 50, in an overtime game on March 4, 2010, against Pittsburgh. He stopped 48 of 49 shots in regulation on April 6 at Carolina.
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DALLAS, TX - NOVEMBER 21: Kari Lehtonen #32 of the Dallas Stars tries to stop a shot against Dominic Moore #28 of...