Rangers left wing Artemi Panarin passes in front of defenseman...

Rangers left wing Artemi Panarin passes in front of defenseman Vladislav Gavrikov against the Carolina Hurricanes at Madison Square Garden on Tuesday. Credit: Corey Sipkin

The last time the Rangers came home after a road trip, they were riding a three-game winning streak, feeling good about themselves and hoping to finally end their futility at home.

Of course, that didn’t happen.

On Saturday night, the Blueshirts were back at the Garden, facing off against the Islanders. They again were coming off a road win and again were hoping they could take all of the good things they’d done in their previous game — a 4-1 victory over the Red Wings in Detroit on Friday night — and apply those to propel them to their first home win of the season.

They entered Saturday at 7-1-1 on the road, but their 5-0 loss to the Islanders dropped them to 0-6-1 at home, and in their six home losses in regulation, they have been outscored 17-1.

The thing is, as they see it, they haven’t been doing anything on the road that they haven’t been doing at home. In their minds, they’ve played the same, home and away, so there wasn’t something they needed to change to fix their home woes.

“I have no idea,’’ said Artemi Panarin, who had a goal and two assists Friday night, when asked why the team has been so much more successful on the road. “Maybe — I don’t know ... Like with last game [a 3-0 loss to Carolina on Tuesday], we looked great the first two periods. Like I said before ... there’s only one way to turn off this thing: Keep doing what we’re doing, keep believing in each other, stay behind each other, right? That’s the only thing we can do.’’

Of course, the big problem at home has been that they haven’t been able to score goals. In their first six home games, they were shut out four times and scored a total of six goals — five of which came in a 6-5 overtime loss to San Jose on Oct. 23.

In many of those games, they thought they had outplayed their opponent, and the analytics — as far as shots on goal, shot attempts, scoring chances and high-danger scoring chances — backed it up.

“For most of the games that we played here, with the exception of a few, I think we’ve been the better team,’’ defenseman Adam Fox said after the loss to Carolina, “especially the ones we haven’t scored.

“I think it’s just a long season. I think it could be just coincidence early that we’re not scoring. But obviously we want to protect home ice a little better and win some games here.’’

Entering Saturday, the Rangers had scored 35 goals and allowed 35 goals in 15 games. Their 2.33 goals against per game was the lowest in the league; their 2.33 goals scored per game was second-lowest.

The hope going into Saturday was that the way they’d won Friday night — they got a goal from Panarin (who had shaved his head to try to change his luck), one from the luckless power play and one from Alexis Lafreniere, who previously scored one goal on 32 shots — finally might carry over to a home win.

Panarin wasn’t quite ready to say that. “Probably my [shaved] head didn’t work for everyone, right?’’ he joked before getting serious. “No, we’ve got to work every night and then every shift to be successful. In my experience, this is the only way. Work.’’

But coach Mike Sullivan, who has changed up his forward lines several times to try to find combinations that work and who still didn’t have center Vincent Trocheck (upper-body injury, long-term injured reserve) available for Saturday’s game, said getting goals from Panarin, Lafreniere and the power play indeed could signal a change for the better for his team.

“Sure,’’ Sullivan said before the game. “I think any time the guys score that we rely on to score, it certainly helps their confidence. It helps their mindset going into the next game.’’

Notes & quotes: Before the game, the Rangers returned D Connor Mackey to AHL Hartford. Sullivan said D Urho Vaakanainen, who missed the previous two games with a lower-body injury, was available to play, though he wouldn’t say if there would be changes from Friday’s lineup ... Igor Shesterkin started in goal after Jonathan Quick played in Friday’s win in Detroit.

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