Schneider made 30 saves and held off the Islanders' late charge to win for the first time since a shutout of Buffalo on Nov. 30.
"I want to win, but you can't do it without the guys in front of you," Schneider said. "I thought we played really well tonight, and we eliminated a lot of their odd-man rush opportunities."
The 27-year-old goalie held the Islanders scoreless until midway through the third period, before Frans Nielsen tied it 1-1.
In addition to limiting the Islanders' odd-man rushes, the Devils capitalized on their own chances.
New Jersey took a 1-0 lead with 8:23 remaining in the first period when Adam Henrique beat Nabokov as the trailer on an odd-man rush.
"We needed this as a group," Schneider said of the win. "We've been stringing some points together, which is nice. But we couldn't settle for one. I think we needed the two."
New Jersey lost to Columbus at home in a shootout on Friday night.
The Islanders absorbed their latest tough home loss. New York hasn't won at Nassau Coliseum in regulation since Nov. 12 -- going 1-5-4 during that span.
This loss came without captain John Tavares, who missed the game because of an undisclosed lower-body injury and had his consecutive games streak snapped at 246. He is day to day.
Despite Tavares's absence, the Islanders controlled the puck and put heavy pressure on the Devils, particularly in the third period. But Schneider turned aside all but one of their 14 shots.
They received a late power play, but couldn't convert -- leaving them 0 for 3 with the advantage during the game.
"It was a typical Islanders-Devils game," New York coach Jack Capuano said. "They got the shot and the bounce at the end."
The bounce resulted in one of two goals allowed by Nabokov, who played another solid game. Fresh off a shutout victory over Detroit on Monday, the veteran goalie made 23 saves.
"It's a process," Capuano said. "[We've] got to do a better job teaching these kids, and they're going to go through some growing pains."
Devils captain Bryce Salvador returned for the first time since he broke a foot on Oct. 22. The 37 year old defenseman logged a team-high 16:05 of ice time in the first two periods. ... New Jersey LW Mattias Tedenby was a healthy scratch. He is minus-5 in three games since he came back from a two-game conditioning stint in the AHL. ... Tavares' consecutive games streak is the fifth longest in Islanders history. ... Islanders 20-year-old center Ryan Strome was held pointless. He has no goals and just one assist six games into his NHL career.