The Islanders got off to the start they wanted, with Sebastian Aho scoring on the team's first shot of the game at 1:41 and Mathew Barzal following it up with a tip on a Robin Salo shot at 13:33.
They were seemingly in control, but Shayne Gostisbehere put Arizona on the board with 44 seconds left in the first period and that seemed to be the spark that ignited the desert dogs.
The Coyotes had a stretch where they recorded 14 consecutive shots on goal from 17:47 of the first period to 9:09 of the second period. That included a pair of goals 14 seconds apart from Clayton Keller, whose centering feed caromed off Scott Mayfield's skate and in, and Nick Bjugstad, who buried a one-timer shortly after. The Islanders did not record a shot until the 9:23 mark of the middle frame, but by that point, the Coyotes were dictating the pace and place of the game.
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"We weren't very sharp and didn't really have much possession or attack and our game sort of second," Brock Nelson said.
Dobson tied the score at 17:45 of the second period, but Travis Boyd put Arizona ahead 4-3 at the 2:08 mark of the third, jamming in a puck in front of Ilya Sorokin, who suffered his fifth-straight regulation defeat - a career long.
Keller scored his second goal of the game at 14:49 of the third period, with his one-timer catching an outstretched Alex Romanov between the legs before deflecting past Sorokin. That held up as the winner as Anthony Beauviller scored a late goal with 1:39 to play.
"I thought we started well, I thought we outplayed them and then I thought when they gained momentum, we had trouble getting it back," Head Coach Lane Lambert said. "I thought we got outworked for a portion of that game. It's unacceptable."