Jamie Langenbrunner and Zach Parise each had three assists while Kevin Weekes made 25 saves in the win for the Devils, who are in the midst of a three-game winning streak.
Andy Hilbert and Sean Bergenheim each had a goal and Joey MacDonald gave up all five goals on 33 shots for the Islanders, who had their first three-game winning streak of the season stopped.
New Jersey's power play, which was ranked second in the league to last coming into the game at 12.5 percent, gave the team the lead. Late in the first with Bruno Gervais in the box for slashing, Johnny Oduya blasted a one-timer from the right point that David Clarkson tipped past MacDonald with just 1:19 left in the frame.
Just 10 seconds later, the Devils grabbed a 2-0 lead as Langenbrunner unleashed a soft shot from the right point that Travis Zajac, charging the net, tipped by MacDonald.
Weekes stopped all nine shots he faced in the first period.
The Islanders got on the board at the 3:29 mark of the second period as Hilbert threw a quick shot on net from the left boards that surprised Weekes.
However, the Devils got the goal back just 23 seconds later as Bryce Salvador's shot from the left point hit off of Chris Campoli's skate in front of the net and past MacDonald.
New York made it a 3-2 game later in the second as Andy Sutton threw a shot on net from the left circle that hit off the right post and was then slammed home by Bergenheim with 6:56 left in the frame.
New Jersey, though, answered with just 16 seconds left in the second as Parise put a shot on net from the left side that was stopped, but Gionta jammed home the loose puck during a scrum in front for a 4-2 advantage.
The Devils struck again on the power play with 7:28 left in the third period as Paul Martin's blast from the high slot went through a screen and into the left corner of the net.