Zuccarello, playing in his seventh NHL game, beat Kari Lehtonen with a nifty hesitation move and wrist shot to help the Rangers improve to 7-2-2 in their past 11. Zuccarello starred again after scoring his first career goal in overtime to beat the Carolina Hurricanes 2-1 on Wednesday night.
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"That's good stuff," Rangers coach John Tortorella said. "No nerves, he just does his job, I think it's terrific."
Zuccarello had decided on a move when he picked up the puck for his shootout attempt.
"I just tried to take a quick deke and a quick release and it was a nice goal," he said. "I'm happy to see that go in. I try to make up my mind, then I look at the goalie and see how he reacts."
Lundqvist had to face Zuccarello during training camp, so he knew Lehtonen would be tested.
"I'm telling you, during camp, he did that all the time," Lundqvist said. "He scored a lot of goals on me in training camp and it was frustrating. The special thing about him is he has a really long stick. He can put it across real fast and get you out of position and put it into the open net. He's really skilled."
Over the summer, the Rangers signed the 5-foot-7 Zuccarello, a native of Norway, after he was MVP of the Swedish Elite League last season.
Zuccarello had 13 goals and 12 assists for the Connecticut Whale of the AHL before he was called up. He has a goal and two assists in seven games for the Rangers.
Lundqvist denied Dallas' Jamie Benn, Brad Richards and Mike Ribeiro in the shootout after making 28 saves through overtime. The Rangers got a short-handed goal from Ruslan Fedotenko and a power-play goal from Artem Anisimov. Lundqvist earned an assist on Anisimov's goal, the goalie's second in two games and third this season.
Ribeiro scored a power-play goal and Lehtonen stopped 29 shots for the Stars, who have won their past six on the road but are 0-3-2 in their past five at home.
"We had a lot of good things in the game. We should probably focus in on the good things," Stars coach Marc Crawford said. "But when you're striving for these points, I guess it's human nature, especially coaches' human nature, to pick at the sores that we've got in our game. We've got to get past that.
"In the end, it's a pretty important point, but we had our hearts set and our minds set on getting this thing righted at home. It's five games now where we haven't won at home."
Brian Sutherby scored an even-strength goal for Dallas, taking advantage of a turnover on a clearing attempt by Lundqvist for the only goal of the first period. Brandon Segal intercepted the puck along the boards behind the net and fed Sutherby, who beat Lundqvist with a one-timer from the right circle at 7:55.
Fedotenko tied it at 1 with 11 seconds left on a Dallas power play, beating Lehtonen with a sharp-angled shot from the right side at 2:49 of the second.
Ribeiro made it 2-1 with 6 seconds left on a power play, scoring from low in the left circle off a pass from Loui Eriksson at 10:20 of the second, but the Rangers kept their cool.
Anisimov capitalized on a boarding penalty on Dallas' Segal, striking from the right circle at 8:04 of the third period to draw the Rangers even.
"There's no panic," Tortorella said. "That's a good sign for a pretty young team, to keep on playing and stay with our concept."
Earlier Friday, the Stars acquired right wing Jamie Langenbrunner from the New Jersey Devils for a conditional pick in the upcoming draft. Langenbrunner was at the game, but didn't play. He is expected to join the lineup Sunday when the Stars play at Minnesota.
Rangers RW Ryan Callahan has begun light skating, but missed his ninth straight game with a broken left hand. ... New York D Michal Rozsival was scratched due to a pulled rib muscle. ... Stars fans booed Rangers LW Sean Avery whenever he touched the puck. Avery had a controversial 23-game stay with the Stars during the 2008-09 season before he was claimed off waivers by the Rangers. ... The Stars were without D Karlis Skrastins and Matt Niskanen, who were injured when they collided while warming up before the third period Wednesday at Chicago. Skrastins has a broken nose and a chipped tooth. Niskanen cut his hand. D Philip Larsen was called up from the AHL Texas Stars. ... The last time the Rangers were in Dallas, the Stars won 10-2 on Feb. 6, 2009.