NEW YORK -- Fans of the New York Islanders have been slow to embrace the franchise's move to Brooklyn. The Islanders themselves are transitioning quite well, especially against the team that poses the biggest threat to their home ice advantage.

Center Brock Nelson and defenseman Nick Leddy scored less than two-and-a-half minutes apart early in the third period Thursday night as the Islanders moved into sole possession of second place in the Metropolitan Division with a come-from-behind 3-1 win over the Rangers at Barclays Center.

The Islanders won both meetings at Barclays Center (they beat the Rangers, 2-1, in a shootout on Dec. 2) to go unbeaten at home against the Rangers for the first time since the 1997-98 campaign.

"We recognize what's at stake here and the rivalry and the intensity of these games," said center John Tavares, who assisted on Leddy's game-winner. "We take a lot of pride in it."

The Islanders rank next-to-last in the NHL in attendance at 13,153, which is more than 2,000 fans fewer than their average crowd last season, the franchise's final at Nassau Coliseum.

But as was the case on Dec. 2, there was no shortage of atmosphere and no empty seats Thursday, when a mixed loyalties sellout crowd of 15,795 turned out at Barclays, which is just a couple subway stops away from the Rangers' home base in Manhattan.

Dueling chants of "Let's Go Rangers" and "Let's Go Islanders" filled the arena. The intensity spilled on to the ice, where the teams combined for nine penalties.

Islanders left winger Matt Martin and Rangers defenseman Dylan McIlrath twice dropped the gloves, though referees interceded before a punch could be thrown. There was also a fracas involving everyone except the goalies less than four minutes into the third period.

"It was the way it always is," Tavares said of Islanders-Rangers games. "The pace was probably the highest you see at all during the regular season. The intensity's there. The crowd's into it. They're always hard-fought."

The two teams combined for 45 shots in an entertaining and fast-paced first two periods before deafening cheers broke out following a goal by Rangers defenseman Marc Staal with 45.4 seconds left in the second.

"I think we were happy with the way we were taking the play to them in the first couple periods," Staal said.

But Nelson scored an unassisted, 4-on-4 goal just 1:53 into the second, when he picked off a clearing pass by Rangers defenseman Keith Yandle and fired a wrister past goalie Henrik Lundqvist.

"If you get that one early, (it) swings that momentum right back in your favor," said Nelson, who collected the first hat trick in Barclays Center history in Tuesday's 5-2 win over the Columbus Blue Jackets. "It kind of deflates you, giving one up late. To come back out the next period and get one, respond, it was big for us."

Leddy gave the Islanders the lead with a power play goal just 2:23 later. Tavares, stationed behind the Rangers' net, passed to Leddy, whose shot ticked off the right post and into the net.

The Islanders, playing without top defenseman Johnny Boychuk (upper body) and Travis Hamonic (lower body), limited the Rangers to just eight shots in the third period before right winger Kyle Okposo scored an empty netter with 1.9 seconds remaining.

"After they scored the second one, it was tough to get to the middle of the ice and get some second opportunities, even get some shots on goal," Staal said. "We were having a tough time getting it into their crease and causing some havoc."

The Rangers scored fewer than two goals for just the second time in their last 14 games.

"I thought it was a gut check for our team," Islanders head coach Jack Capuano said. "I thought we played extremely hard against a good team. With Hamonic and Boychuk being out, they picked up the slack."

With their second straight win, the Islanders (24-15-5) broke a tie with the Rangers (23-15-5) for second place in the Metropolitan Division and improved to 15-7-2 at home. Only four other teams have more wins at home.

"You want to be comfortable and know that you have the crowd behind you at all times," Nelson said. "Get that momentum, you can feed off them for 41 games throughout the year. We're trying to do that right away and trying to do that early. And I think we were able to kind of see that today in the third."

Islanders goalie Jaroslav Halak made 34 saves and improved to 8-0-0 in his career against Lundqvist, who made 29 saves.

NOTES: The Islanders scratched D Travis Hamonic, who is expected to be out until the All-Star break with a lower-body injury, as well as RW Steve Bernier and D Scott Mayfield. ... Islanders Hall of Famer Mike Bossy scored his 400th career goal 32 years ago Thursday in a game against the Rangers. He was in attendance Thursday night. ... The Rangers scratched D Dan Girardi (cut right hand) and C Oscar Lindberg. ... Rangers G Henrik Lundqvist made his 10th straight start, his longest streak since head coach Alain Vigneault took over before the 2013-14 season.