The Islanders were coming off a 4-0 loss to the Vancouver Canucks on Sunday and managed one goal on 25 shots through two periods against the Coyotes. Arizona, which has lost seven straight, put on pressure early in the third period but couldn't get the go-ahead goal, and the Islanders suddenly found their scoring touch.
"Even if we're down one or two, we still know that we're capable of coming out; we have a lot of threats on our team and we have to be confident in ourselves," Boychuk said. "It's a good feeling when you come out and explode like that."
Martin broke a 1-1 tie at 3:18 off a broken play. A good forecheck by New York's fourth line freed the puck. It came into the left circle, and Martin quickly sent a high shot past goaltender Mike Smith for his eighth goal of the season. Boychuk made it 3-1 when he drifted into the high slot, took a pass from John Tavares and beat Smith with a slap shot for his seventh.
"There was a 4-on-3 or 4-on-2 and I saw a chance to jump up in the rush at the right time," Boychuk said. "Johnny made a good pass, and all I had to do was hit that blocker side because he had come out a little bit and I saw that side open."
"It's an unbelievable feeling," said Mouillierat, who was credited with his first NHL point, an assist, after a scoring change on Martin's goal. "You play so long and especially at my age to get my first crack at the NHL, there are times in the minors you think it's never going to happen and when it does, it's a pretty incredible feeling."
Brock Nelson capped the outburst when he batted a rebound past Smith at 9:10 for his 17th of the season and New York's fourth goal in a span of 5:52.
Anders Lee also scored for the Islanders (40-20-2), who had lost two in a row, and kept them two points ahead of the New York Rangers in the race for first place in the Metropolitan Division. Goaltender Chad Johnson made 27 saves.
The Islanders have 40 victories in a season for the first time since 2006-07. They haven't made the Stanley Cup Playoffs in a full 82-game season since.
Mark Arcobello scored in the second period and Smith made 34 saves for the Coyotes (20-34-7), who haven't scored more than two goals in their past 10 games. The Coyotes, playing the second half of a back-to-back and their third game in four nights, appeared to run out of energy in the third period; that may partly have been the result of absorbing 42 hits by the Islanders in the first 40 minutes. They repeatedly turned the puck over in the final period, something that didn't escape the notice of coach Dave Tippett.
"Our turnovers played a role in the third, our turnovers and inability to think and read rush plays," he said.
Smith said the Coyotes' performance was a step back from their play in a 2-0 loss at the New Jersey Devils on Monday.
"I'd say so," he said. "We were fine for 40 minutes. I thought we did some good things again. We weren't as crisp as we were (Monday) night, but that's to be expected. We were in a hockey game though.
"Then we completely self-destructed. To win in this League is hard, to score goals is tough, but at the end of the day, you're in a 1-1 hockey game in the third period on the road. That's a pretty good position to be in. Then a turnover in the neutral zone and it's in our net … then we give up a 4-on-2, and the rest is history from there."
The Islanders outshot the Coyotes 12-6 in a fast-moving first period that went 5:48 from puck drop until the first whistle. The Islanders attempted 28 shots but saw half of them blocked by the Coyotes.
But New York went ahead 37 seconds into the second period.
Defenseman Travis Hamonic raced down the right side and threw a hard pass toward the slot, where Lee was unchecked. He stopped the puck with his skate, turned and sent a backhand shot past Smith for his 20th goal of the season, one behind League leader Filip Forsberg of the Nashville Predators, who scored his 21st later Tuesday.
"If you go to the net, you're going to get some goals," Islanders coach Jack Capuano said of Lee. "When you see a guy who goes to the net like that, good things are going to happen. He does it every day."
Arizona tied the game at 15:52, taking advantage of David Moss' takeaway from Tavares in the Coyotes zone. Moss sent the Coyotes up ice 3-on-2, and Martin Erat set up Arcobello for a one-timer from the top of the left circle that went past Boychuk's attempted block and beat Johnson to the short side. It was the 12th goal of the season for Arcobello and his fourth in six games with Arizona, the fourth team he's played with for this season.
But the Islanders' third-period blitz sank the Coyotes and left Smith shaking his head.
"It's embarrassing. I've never been so embarrassed as I have been this year to walk into arenas," he said. "I've had enough of it. It's simple plays that have to be made. When they don't get made and come back in your net, it's frustrating.
"Guys are trying, but it's got to go to a different level. It's not close enough to give ourselves a chance to win."