The Coyotes took a 1-0 lead 2:21 into the first period when Kyle Chipchura beat Martin Brodeur.
Chris Summers gave the Coyotes a 2-0 lead when his slap shot got through Brodeur with 3:03 left in the second period.
With 0.3 seconds left in the second period, the Devils cut the lead to 2-1 on a Ryane Clowe deflection.
The Devils tied the game with 9:28 left in the third period when Adam Henrique scored on a wrap-around to make it 2-2.
Mikkel Boedker of the Coyotes scored in the first round of the shootout, and it held up as the game-winning goal.
For the full recap, visit SNY.tv.
The Devils are off Friday.
They visit the Islanders Saturday at 7:00 p.m.