GLENDALE, Ariz. -- Arizona coach Dave Tippett has a simple formula for handling his goaltending situation these days, which bodes well for Louis Domingue.

"Right now, we're in the position -- you win, you're in," Tippett said.

"He won. He's in."

Domingue stopped 25 shots for his first career shutout and defenseman Oliver Ekman-Larsson scored in the first period in the Coyotes' 1-0 victory over the New York Islanders on Saturday night at Gila River Arena.

Domingue, making his first start of the season, denied a short-handed breakaway chance by defenseman Casey Cizikas early in the second period, his most difficult stop, while plugging the dike.

The Coyotes (15-15-2) had given up 37 goals in their previous eight games, losing six. Starting goalie Mike Smith is expected to miss eight to 10 weeks after undergoing abdominal surgery this week and backup Anders Lindback was ill.

"I got prepared my whole life for this game," said Domingue, who had four starts and seven appearances with the Coyotes last season.

"I'm ready to get my chance here. I'll go a day at a time, but it was good tonight. This game was a real confidence booster. Every time you play and you do well, you feel like you belong in this league, and that's how I feel right now."

Domingue made his season debut Thursday when he gave up two goals in 28 minutes in relief of Lindback in a 7-5 loss to Columbus.

The Islanders' first shot, by Frans Nielsen, hit the post, but that was as close as the Islanders (18-11-5) were to get. They were shut out for the first time this season and have lost three games in a row after getting a point in 10 straight. They have not scored in the third period in their last six games.

"I thought the key point of the game was the breakaway that Louis stopped," Tippett said. "Our bench was like alive. He was calm in there. He moved the puck very well. Just real steady. You get a good game like that, it rubs off on everybody."

Jaroslav Harak made 28 saves for the Islanders, who were 0 of 3 on the power play.

Detroit, Minnesota and Boston are the only teams that have not been shut out this season.

Ekman-Larsson combined with right winger Anthony Duclair for the only goal at 17:59 of the first period. Ekman-Larsson dropped the puck to Duclair along the left boards and skated into the slot, where he took a return pass from Duclair and scored on a one-timer.

Ekman-Larsson's goal was his seventh this season, his fourth game-winner. He leads NHL defensemen with 20 game-winning goals since his first year in the league in 2010-11.

"We did a real good job of defending in front of our net," Ekman-Larsson said. "Louis played unbelievable back there. Everybody felt comfortable with him between the pipes there."

The teams combined for 14 shots in the first period, and the Islanders did not get off a shot during the only power play of the period.

"We need to find a way to score," said Islanders center John Tavares, who had two shots. "You don't take anyone for granted in this league, and I don't think we did. He (Domingue) played well, and we need to find a way to generate more."

NOTES: Islanders RW Kyle Okposo, who has eight goals and a team-high 26 points, missed a game for the first time this season because of a lower-body injury. He also is expected to miss Monday's game against the Anaheim Ducks. ... Coyotes D Zbynek Michalek (lower body) missed his third straight game. ... Coyotes C Martin Hanzal, third on the team with 20 points, returned after missing four games with lower-body injuries. He has missed six games this season. ... The Islanders won the first game of the two-game series, 5-2, at Barclays Center on Nov. 16. ... Coyotes RW Anthony Duclair returned after missing the 7-5 loss to Columbus on Thursday. ... The Islanders' other scratches were LW Eric Boulten and D Brian Strait.