"Four wins going in [to the Christmas break] is about as good as you can ask for," Hall said. "For a lot of those four games, we've carried the play and played the way we wanted to. The games are only going to get harder now and I think we are ready for that."
Chicago (17-13-5) lost its second straight after a five-game winning streak.
The Blackhawks lost both games in the season series against the Devils; they blew a three-goal lead in a 7-5 loss in Chicago on Nov. 12.
Chicago goaltender Corey Crawford was pulled from each game. He made four saves on seven shots Saturday before being replaced at 13:22 of the first period. Crawford made 19 saves on 25 shots in the first game.
Anton Forsberg made 21 saves in relief Saturday.
Boyle scored from the slot to make it 1-0 at 2:48 of the first period, and Palmieri made it 2-0 on the power play at 9:20.
Zacha's one-timer from the slot made it 3-0 at 13:22.
Kane said he thought the Blackhawks could have built on his goal.
"It looked like that could have been a big goal for us," he said. "We had things going on there in the second. We had chances. We had opportunities. When you get one and you're down two, maybe the comeback is on. It's unfortunate it didn't happen that way."
Instead, the Devils took a two-goal lead into the third, and Hall scored on a breakaway 2:02 into the period to make it 4-1.
"Sometimes in hockey, in sports, momentum gets away from you and you start really playing on your heels and you are not comfortable with the puck and playing the way you want to," Hall said. "Sometimes, you have to take a deep breath and that is what we did in the second intermission. I think that goal can settle down our group a bit. Whether it's a goal, a big hit, a good play. You need that play to just turn momentum around."