Jaromir Jagr saved the Devils with his eighth goal of the season that came with only 61 seconds left in regulation and Zajac came through to give them back-to-back victories.
Anaheim lost its fifth straight, but this was the Ducks' first setback at home this season.
A pair of power-play goals in the second period by Nick Bonino and Ryan Getzlaf rallied Anaheim from a 2-1 deficit, but Jonas Hiller was unable to hold onto the lead. Hiller gave up the four goals on 25 shots
Martin Brodeur has bounced back from a slow start this season and made 22 saves to earn his seventh victory in 10 decisions. His NHL regular-season record victory total climbed to 676.