Rangers goaltender Igor Shesterkin stands in front of the net...

Rangers goaltender Igor Shesterkin stands in front of the net after New Jersey Devils defenseman Dougie Hamilton scored in the second period of an NHL game at Madison Square Garden on Monday. Credit: Kathleen Malone-Van Dyke

The Rangers keep starting games poorly and keep giving up odd-man rushes. And no matter what they do, they can’t seem to figure out how to turn things around.

On Monday night against a Devils team that is fully healthy now and backed by a true No. 1 goalie, all the Rangers’ warts were exposed and punished, as the team from across the Hudson River came into Madison Square Garden and thrashed their big-city rivals, 5-1, behind two goals and an assist from Jack Hughes, a goal and three assists from Jesper Bratt and a standout performance between the pipes by Jacob Markstrom, their prized summer acquisition.

The Rangers fell behind 2-0 in the first period and when they started playing well and generating pressure, Markstrom (38 saves) kept them at bay, dooming them to their sixth loss in the last seven games and 10th in the last 18.

It left the Rangers at 13-10-1 and left some shell-shocked faces in the home locker room.

“Everyone in here has got to just play a little bit out of their comfort zone,’’ center Vincent Trocheck said after a long pause. “Obviously, what we’re doing right now isn’t working, so it’s gonna take something different.

“Guys that are usually playmakers and scoring goals have got to chip it in, grind it out. Guys that aren’t usually hitting have got to start hitting. We’ve just got to play out of our comfort zone, got to dig our way out of this.’’

Coming off their last-minute, 4-3 win over Montreal on Saturday night that ended a five-game losing streak, Rangers coach Peter Laviolette was forced to juggle his forward lines when rookie Brett Berard was unavailable due to an upper-body injury.

So the coach reunited the Artemi Panarin-Filip Chytil-Alexis Lafreniere line from last season, and used that as his top trio. Will Cuylle and Kaapo Kakko flanked Trocheck on the second line and the former top line of Chris Kreider, Mika Zibanejad and Reilly Smith dropped to the third spot.

But the new look did not work. The Rangers fell behind 1-0 on Bratt’s goal 1:27 into the game. Bratt took a pass from Ondrej Palat in his own end, skated past Lafreniere in the neutral zone, and broke in two-on-one with Hughes against K’Andre Miller. Bratt shot the puck from the lower part of the left circle and beat Igor Shesterkin (23 saves) between the pads for his 12th goal of the season.

“I hate the first goal,’’ Laviolette said after a 15-minute delay in meeting the media for his postgame news conference. “I just talked about not giving up odd-man rushes from the offensive zone, and we did.’’

“If everyone’s doing their job, you don’t get those odd-man rushes,’’ defenseman Adam Fox said. “The ‘D’ could still go down the wall and get backed up [by a teammate].’’

Dawson Mercer’s goal at 7:10 of the first period made it 2-0, Devils, but then the Rangers dug in and began to shift the momentum and create chances. That’s when Markstrom stood tall, making 12 saves to keep the Rangers off the board in the period.

“I thought we could have scored two or three at the end of the first, and you leave the first period and you’re down 2-0,’’ Laviolette said. “That’s not the way you want to start a division game against the Devils. It’s not good. It’s not where we want to be. And, you know, then from there, they scored a couple on the power play. And so it just .  .  . it never found its groove.’’

The game was still within reach going into the second period, but when Smith — back in the lineup after being a healthy scratch last game — took a tripping penalty at 7:05, and Fox was called for hooking at 8:44, that gave the Devils a five-on-three power play. They capitalized on the man-advantage as Dougie Hamilton scored to make it 3-0 at 9:04. Hughes then banged in the rebound of a shot by his brother, Luke Hughes, to make it 4-0 at 12:38.

Kreider’s power-play goal at 13:29 of the second briefly gave the home fans something to cheer about, but Hughes’ second goal, a shot through a screen by Nico Hischier on a four-on-three power play at 18:56 of the period, quieted them down again.

Notes & quotes: Shesterkin fell to 8-9-1 this season .  .  . Forward Jimmy Vesey was a healthy scratch as Jonny Brodzinski took his place in the lineup. D Chad Ruhwedel was the other scratch .  .  . Chytil, who started the game as the No. 1 center, played just 11 minutes, 47 seconds, and by the third period was back between Cuylle and Kakko, with whom he’s played most of the season. Trocheck also returned between his regular linemates, Panarin and Lafreniere.