Islanders players celebrate a goal by Islanders center Anthony Beauvillier...

Islanders players celebrate a goal by Islanders center Anthony Beauvillier against Rangers goaltender Ondrej Pavelec in an NHL hockey game at the Barclays Center on April 5, 2018. Credit: Kathleen Malone-Van Dyke

John Tavares heard the Barclays Center crowd chanting his name in the third period and again said he hopes it works out that he’ll remain an Islander.

If not, Thursday night’s 2-1 win over the Rangers will stand as the impending unrestricted free agent’s last home game for the franchise that selected him first overall in 2009.

“I’ve always been treated, since Day 1, very well,” said Tavares, the Islanders’ captain since 2013. “They’ve always stuck by me and have been really proud to have me here. It’s made it a lot easier for me to just kind of grow into the kind of player and person I am. I’m just appreciative of that.

“I’m not trying to look at it as if it’s the end. That hasn’t been determined. I’ve always wanted it to work out and stay. That’s still what I hope transpires. That’ll come in the time ahead.”

Tavares had his point streak snapped at four games as the Islanders (34-37-10) won two straight for the first time since Feb. 15-16. They leapfrogged the Rangers (34-38-9) out of last place in the Metropolitan Division and moved into seventh by one point. Still, the Islanders are 5-12-4 since Feb. 19 and will miss the playoffs for the second straight season.

The Islanders swept the four-game season series from the Rangers, who have lost all six games they have played at Barclays Center. The Isles are 11-1-0 against the Rangers since the start of the 2015-16 season and have won seven straight overall.

“I heard some of the chants during the game, which is really nice of the fans,” Tavares said. “I’m just trying to finish the season like I started the season and played the whole year. So the emotion is really the same. It’s just disappointing knowing we’re not playing past Saturday.”

Tavares is completing a six-year, $33-million deal and has kept a solid poker face all season as to his intentions, or even whether he’s leaning toward returning or testing the market.

It’s been the question that’s hung over the whole season.

“We hope that’s not the case,” Islanders coach Doug Weight said of this potentially being Tavares’ last home game as an Islander. “To get too deep into that thought process is not healthy for me or anybody else.”

Weight said the trepidation about Tavares’ ultimate decision probably was more pronounced at the beginning of the season.

“He’ll make a decision when he makes it,” Weight said. “I don’t have nerves. Anxiety is probably a closer word. With or without him, we’re going to move forward and try to win. We’d like him here.”

Notes & quotes: Goalie Jaroslav Halak made 34 saves and improved to 18-7-0 lifetime against the Rangers . . . Anthony Beauvillier extended his goal-scoring streak to five games as he scored the winner at 7:27 of the second period . . . Defenseman Thomas Hickey had the Islanders’ first goal at 4:55 of the second period . . . Right wing Shane Prince, activated off injured reserve, logged 10:00 after missing 33 games with a lower-body issue . . . Right wing Tanner Fritz (illness) was not available . . . Weight said defenseman Johnny Boychuk’s season is over. Boychuk has been dealing with a lower-body issue that might require offseason surgery . . . Casey Cizikas was presented this season’s Bob Nystrom Award as the Islander who best exemplifies leadership, hustle and dedication.

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