ELMONT, N.Y. -- Ilya Sorokin made 14 saves, and Mathew Barzal scored for the New York Islanders in a 1-0 win against the Arizona Coyotes at UBS Arena on Tuesday.

It was the first shutout of the season for Sorokin, who led the NHL with six last season.

“I just heard about the 14 shots. I didn't really know because it felt like they had some chances,” Barzal said. “I thought they pressed a little bit offensively tonight, so I think we got some good saves from Sorokin, and I think they fanned on a couple. ... But I mean, we're always going to be pretty solid defensively the way our system is.”

ARI@NYI: Sorokin shuts out Coyotes at home

Noah Dobson and Kyle Palmieri each had an assist for New York, which is 2-0-0 to start a season for the first time since 2014-15 (4-0-0).

“I thought we battled and I thought our structure was great,” Islanders coach Lane Lambert said. “They're a dangerous team. They had a couple of opportunities, but when they did, our goaltender came up big for us. A total team effort."

Karel Vejmelka made 33 saves for Arizona (1-2-0), which was coming off a 2-1 loss at the New York Rangers on Monday.

“We didn’t execute at all," Coyotes coach André Tourigny said. "We started the game by trying to do too much. Each line has to find their own identity. Not everyone can play that high-possession game. We need to put pucks on the net.”

Barzal scored a power-play goal at 3:47 of the second period, beating Vejmelka over his right shoulder with a one-timer from the top of the left circle.

ARI@NYI: Barzal nets opening goal for Isles

It was the first power-play goal of the season for the Islanders, who ranked 30th in the NHL with the man-advantage last season (15.8 percent).

“I think we've definitely had our looks. We've been really working on it,” Dobson said. “It’s nice to get rewarded, and I think that’ll bode well for the confidence moving forward. I think we got the schneid off our back. We got to build on it and keep getting better."

New York outshot Arizona 24-7 through the first two periods.

"I don't think we shot enough pucks," Coyotes forward Jason Zucker said. "... I thought we did a lot of good things. We forechecked hard, we got pucks back, we were playing fast. I think our mentality is to hold on to pucks a little too long. We have to start getting some pucks on net."

NOTES: Sorokin got his 17 NHL shutout, passing Rick DiPietro for third in Islanders history. Glenn Resch is first with 25, and Billy Smith is second with 22. ... New York forward Matt Martin played his 900th NHL game, finishing with two hits in 7:39 of ice time. ... Islanders defenseman Scott Mayfield did not play because of a lower-body injury. ... Arizona will conclude its season-opening four-game road trip at the St. Louis Blues on Thursday.

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