Schneider, who was selected as an All-Star for the first time in his career, is 12-6-2 in 20 starts on the road this season.
Reid Boucher scored early in the first period for the Devils, who won for just the second time in the past seven games.
Kyle Palmieri scored his team-leading 18th goal of the season 18 seconds into the third period. Joseph Blandisi was able to get a stick on the puck behind the net and tap it out to Palmieri, who stuffed a close-range shot past Coyotes goalie Anders Lindback.
Arizona was shut out for only the second time in 44 games this season.
Lindback had 14 saves. It was his first start in goal for Arizona since giving up three goals on five shots in one period on Dec. 29 against Chicago.
Boucher, recalled by New Jersey on Friday for his second stint in the NHL this season, opened the scoring with his first goal at 3:52 of the first period. Boucher has played in only four games with the Devils this season.
Former Coyote Lee Stempniak assisted on the goal for his 400th point.
The Coyotes entered the game having scored on 7 of their past 14 power plays before going 0-for-5 against the Devils.
The Devils failed to score on the man advantage for the seventh straight game and are 0 for 17 in that stretch.
NOTES: Saturday's game was moved from the evening to noon local time with the NFL's Arizona Cardinals playing in a playoff game next door at University of Phoenix Stadium in a night game. . Defenseman Kevin Connauton made his Coyotes debut after being acquired off waivers on Wednesday. Defenseman Jarred Tinordi, picked up in a trade with Montreal on Friday, was scratched, along with healthy scratches Viktor Tikhonov and Klas Dahlbeck. . Devils F Bobby Farnham served the second of his four-game suspension and joined recently recalled C Brian O'Neill and C Stefan Matteau as scratches.