The Penguins are 6-1-1 in their past eight games despite missing several key players, including forward Evgeni Malkin, who did not play Friday (upper body).
WATCH: All Devils vs. Penguins highlights
"We have some difference-makers," Penguins coach Mike Sullivan said. "It starts with Sid. When you can build around a guy like that, I think that really makes your team better and the people around you better."
In a busy first period, Phil Kessel, Jake Guentzel and Crosby scored for the Penguins to give them a 3-2 lead. Kyle Palmieri and Stefan Noesen scored for the Devils (26-32-12).
Palmieri gave New Jersey a 1-0 lead at 5:35. Skating in alone on Matt Murray, he used a shot fake to freeze the goaltender, went backhand to forehand and wrapped a shot around Murray's left pad.
"I thought we got some goals at some key times," Devils coach John Hynes said. "We had some good looks. … We have a little bit more team speed now. They've been much more tenacious in the offensive zone, and also some of our zone entries and line rush plays have been good. We've gotten more chances and it's good we were able to capitalize."