Nick Schmaltz had a goal and an assist for the Coyotes (23-46-5), who have lost four straight and 11 of 13 (2-10-1). Karel Vejmelka made 32 saves.
Coyotes forwards Nathan Smith and Jack McBain moved up from college hockey to make their NHL debuts.
"They worked hard, they competed. But I wanted a little bit more from our older guys, personally," Arizona coach Andre Tourigny said. "I want them more engaged. Our young guys need role models, and I felt our team worked but needed more of a push."
Smith played for the Coyotes three days after playing for Minnesota State in a 5-1 loss to Denver in the Frozen Four final. McBain played this season for Boston College.
Smith took one shot and played 20 shifts in 14:02. McBain played 24 shifts in 13:45. Each player was minus-1.
"It's a dream come true, but an unfortunate result," McBain said. "Obviously it's been different for us coming in from college, but the guys and the coaching staff have been great, making adjustments."
Schmaltz tied it 2-2 at 18:36 of the second period, the only goal for Arizona on its four power plays.
The Devils answered with four consecutive goals. Tatar scored 38 seconds later at 19:14 to make it 3-2. The Coyotes turned the puck over and Tatar's wrist shot from the left-wing boards got past Vejmelka, who was scrambling to get back to the net.