Green was promoted from associate coach to replace Lindy Ruff on Monday.
Nick Cousins scored two goals, Matthew Tkachuk had three assists, and Anthony Stolarz made 22 saves in his first start in three games for the Panthers (43-16-4), who won their sixth straight.
Florida, which won 4-2 at the New York Rangers on Monday, is 16-2-0 since Jan. 22 and became the first team to reach 90 points this season.
"We have a game plan each night and guys go out there and execute," Cousins said. "It's been a lot of fun coming to the rink. Everybody's pulling on the same rope, and we’ve got four lines that are contributing every night. It's different guys every night. I mean, when you do that, you have success, so it's a lot of fun right now. We’ve just got to make sure we keep it going."
Jack Hughes had a goal and an assist, Jesper Bratt had two assists, and Akira Schmid made 26 saves for the Devils (30-28-4), who have lost three straight and four of their past five.
"I thought we showed more energy and were harder on pucks, but there were spurts when we were good at that and there were other spurts in the game where we weren't as good," Hughes said. "So, we'll have to continue to work on that."
Green said: "Our guys didn't have a lot of plays with the puck, and any time you don't pass the puck well and receive the puck well, it's really hard to get a lot of traction in your game. I thought we started to play a little better (in the second period) with the puck."