Nelson scored at 1:22 of the third period with a wrist shot from the right circle after a lob pass from Bailey to give New York a 3-0 lead, then made it 4-0 on a sliding redirection of Anthony Beauvillier's feed at 9:59.
Sorokin preserved the shutout with a pad save on Liam O'Brien's wrist shot with 1:52 remaining.
New York outshot Arizona 21-4 in the third period.
"I think that's the style we want to play," Mayfield said. "When we got in their end, we were able to control the puck. We didn't give them easy exits coming back in the neutral zone, stuff like that. We did a good job offensively, and that's sometimes your best defense. But in our zone, I think we played physical, blocked shots and then we were able to exit the zone pretty cleanly."
NOTES: The Islanders announced immediately following the game that Clark Gillies, who won the Stanley Cup four times in a row from 1980-83, died Friday. He was 67. … Islanders center Casey Cizikas left the game at 6:24 of the third period with an undisclosed injury, and forward Oliver Wahlstrom did not receive a shift in the third period. "They're both fine," Trotz said. "[Wahlstrom's] fine. It was a coach's decision that he didn't get a shift." … Czarnik was plus-3 in 13:59 of ice time after being recalled from the taxi squad. … Coyotes forwards Travis Boyd, Nick Schmaltz and Clayton Keller, and defenseman Anton Stralman, were minus-3. … New York was playing the first of a seven-game homestand. … Each team was playing the first of back-to-back games. The Islanders play the Toronto Maple Leafs and the Coyotes are at the New York Rangers on Saturday.