Scatchard had a goal and an assist in the second period for his first two-point game this season. Nagy assisted on each of the Coyotes' first two goals. Derek Morris and Owen Nolan also scored for Phoenix.
Playing nearly airtight defence in front of goalie Curtis Joseph, the Coyotes limited New Jersey to 15 shots. John Madden scored for the Devils.
The Coyotes broke on top just past the halfway mark of the opening period. Jeremy Roenick, on his off wing, fed a crashing Morris in the right faceoff circle with a perfect pass. Skating into the pass, Morris beat Martin Brodeur with a rising slap shot at 13:17.
Despite managing only one shot in the first 12 minutes of the game, the Devils generated several good scoring chances against Joseph late in the opening period. Joseph stopped Jay Pandolfo from the slot on a 2-on-1 and later gave Brian Gionta, with the puck on his stick, no room in front of the net.
Madden tied the score early in the second period when he knocked the puck in during a goal-mouth scramble at 1:58.
Phoenix responded with consecutive goals.
First, Scatchard gave the Coyotes the lead when he tipped in Ed Jovanovski's shot from the right point at 4:30. Then, Nolan beat Brodeur short-handed when he converted Scatchard's pass off the right-wing boards at 10:38. The short-handed goal was the Coyotes' second of the season.
During the final period, the Devils managed only one solid chance against Joseph. Scott Gomez was stopped in close with about six minutes remaining.
Notes: Mike Ricci returned to the Phoenix lineup for the first time this season. The centre was out with a neck injury and rehabbed for two games at San Antonio in the AHL. The crowd of 12,883 was the second-lowest for a Phoenix home game this season.