Sam Reinhart scored for the Sabres, whose wild-card playoff chances took a hit with a second loss in three days. Carter Hutton made 20 saves as Buffalo fell six points behind Pittsburgh in the race for the final wild-card spot.
The win was Schneider’s second in three days. His win in relief against Minnesota on Friday was his first since December 2017, the same month he had a five-game winning streak.
Schneider had been struggling to regain his form after being limited by a hip problem that required offseason surgery.
After a scoreless first period, the Devils jumped to a 2-0 lead as Palmieri set up on goals by Wood and Bratt.
Wood got the first one from right in front at 7:25 of the second with a quick rush up the ice. He sent a pass to Travis Zajac who tipped it to Palmieri, who found Wood coming down the middle of the ice for his sixth goal.
Bratt doubled the margin with 6:22 left in the period early in a power play. He took a pass from Palmieri in the right circle and one-time a shot past Hutton for his sixth goal.
The Sabres got back in the game with 56 seconds left in the second when defenseman Zach Bogosian made a nifty, cross-ice pass to Reinhart for a shot into an open net.
Palmieri iced the game with his team-high 26th goal. He broke in on the right side and roofed a shot from the faceoff circle. Joey Anderson added a short-handed, empty-net goal with 3:09 to play.
NOTES: Sabres C Casey Mittelstadt returned to the lineup after missing two games with a lower-body injury. … Devils captain Andy Greene left the ice in the first period after being hit by the puck near his facial area. He returned later in the period. … Devils C Pavel Zacha missed his first game since early November with an upper-body injury. … New Jersey has a power-play goal in five straight games.
Sabres: Start a Florida swing, playing the Panthers on Tuesday night and Lightning on Thursday night.
Devils: Host Pittsburgh on Tuesday night, looking to sweep their four-game season series.