Palmieri swooped in and hammered home a rebound to get the Devils back on even terms only 44 seconds into the middle frame.
"A couple fortunate bounces on the two there but it was good to contribute in that way," he said. "Had a couple opportunities in the last couple of games and it's good to see those go in."
Less than a minute after Palmieri's game-tying marker, Freddy Claesson's shot from the point beat Shesterkin glove side to put New Jersey in the lead for the first time tonight.
Mike McLeod was called for tripping to give the Rangers power play a chance to get back on even terms but Devils killed their third penalty of the game.
"Our penalty kill's been playing great," Palmieri remarked. "They've done a great job. A lot of times it's your goalie who's your best penalty killer but those guys go out and play for each other and make sure that the puck stays out of our net."
Palmieri fed Wood on a partial breakaway but his shot was turned away by Shesterkin with 5:14 to go in the second. On the play, Adam Fox was called for tripping to send the Devils on their first power play of the game.
Devils capitalized as Travis Zajac redirected a feed from Hischier top corner on Shesterkin to make it 4-2. The lead was extended to 5-2 25 seconds later after John Hayden redirected a point shot from Severson to put the Devils up by three.
"We've been playing some good hockey for the last little while here and because of that we've got some confidence in these situations and are able to beat real good teams," Zajac said.
Shots in the second were 14-11 for the Rangers but Devils outscored the home side 4-1 in the period.
"Really strong period. It's not like we hated our first period. They came out flying and capitalized on a couple chances but in general it wasn't that bad of a period," said Nasreddine.
Rangers pulled to within a pair of goals after Brendan Smith's shot from the left point was tipped way to the net by Greg McKegg and beat Blackwood with 6:18 to go in the third.
With 55.7 seconds to go, Zajac took advantage of a Fox giveaway at his own blueline to put the puck into an empty net.
Twelve seconds later, the Rangers scored to draw back within two. But that was as close as they would get.
"There was a lot of motivation coming in. The confidence was really high after a really good game against St. Louis. Sometimes you win and don't deserve it but we played really well against the Blues last night," Nasreddine said.
"Back-to-back wins against two teams that were really hot. Blues eight-game winning streak and Rangers probably the hottest team in the League."