Jean-Gabriel Pageau had four points, including a natural hat trick, and Kyle Palmieri had a goal and two assists for the Islanders (32-27-9), who have won four in a row.
New York is 11 points behind the Washington Capitals for the second wild card into the Stanley Cup Playoffs from the Eastern Conference with one game in hand.
"It's funny, a little over two years ago was my last game in the League in this building, so I don't know if it's fate or coincidence, but I'm just grateful for the opportunity," Schneider said. "It's easy to take the League for granted when you're young and playing a lot, but things can change quickly so always be grateful for the chances you get.
"I thought my teammates worked really hard to make my first game back in a long time as easy as possible."
Nico Daws made 25 saves for the Devils (24-39-6), who have lost five of their past six.
"I thought we were really flat in the first period," New Jersey coach Lindy Ruff said. "Maybe we were having a pity party from the night before (a 7-6 overtime loss to the Florida Panthers on Saturday) where we felt pretty bad about the way that game ended."
Pageau gave the Islanders a 1-0 lead at 11:56 of the first period on a snap shot from the slot. He made it 2-0 at 14:00 with a power-play goal.
Pageau completed the hat trick from the slot at 14:58 of the second period for a 3-0 lead. His last three-goal game was with the Ottawa Senators in a 4-2 win against the Devils on Nov. 13, 2019.
"I got a few bounces tonight," Pageau said. "I think our line (Josh Bailey-Pageau-Palmieri) has been doing a really good job the past few games. I think you start worrying when you don't have chances, and we've had chances."