Andrei Loktionov and Patrik Elias each posted a goal and an assist for the Devils, who have won three of their last four. Ilya Kovalchuk had the other goal while Johan Hedberg made 23 saves.
"We had a lot of chances tonight and did a good job of putting them away," said Kovalchuk. "Hopefully this gives us a big jump and we'll be able to carry it into Philly."
Jakub Voracek and Scott Hartnell scored for the Flyers, who were coming off a win against Buffalo on Sunday but fell for the fourth time in the past five games. Ilya Bryzgalov was tagged for all five goals on 32 shots.
"They beat us tonight and that's all there is to it," said Bryzgalov. "I really have no idea what to say about this aside from that I'm just tired and have no emotions. A lot of disappointment right now."
These two teams will meet in Philadelphia on Friday.
The Devils grabbed the lead just 2:02 into the game as a turnover in the Philly end resulted in Elias eventually getting the puck down low and slipping in a backhand.
Philly tied the game on the power play near the midway mark of the first as Wayne Simmonds passed it from the low left side to the right circle where a cutting Voracek one-timed it home.
Just 36 seconds after the Flyers tied the game, Henrique snapped a wrister from the right circle that went off the right pad of Bryzgalov then hit off Matt Read before going into the net.
Kovalchuk made it a 3-1 game while shorthanded as Read was unable to keep the puck in the zone and it went the other way. Kovalchuk caught up to the disc in the Flyers end down the right wing and snapped a wrister that beat Bryzgalov to the glove with 2:42 left in the first period.