UNIONDALE, N.Y. (AP) -- New York's latest loss to the Philadelphia Flyers was very fresh in the minds of the Islanders when it appeared they were headed for another one in the home-and-home rematch.
Out of nowhere, the Islanders stormed back from a two-goal deficit in a dominant third period and handed the Flyers the kind of loss they have been pinning on opponents all season.
Kyle Okposo scored the tying goal on a power play late in regulation and then netted the decisive tally in the shootout for the Islanders, who rallied past Philadelphia 4-3 Monday to earn a rare win over the Flyers.
Philadelphia came back in the third period at home on Saturday to beat the Islanders 6-4. It was the Flyers' team-record tying ninth win this season after they trailed at some point in the third period.
Okposo also assisted on captain John Tavares' power-play goal in the second.
''We came up with good plays when we needed them most,'' said Okposo, who has four goals and three assists in seven games since his daughter was born. ''We wanted to come back after the game at Philly, and we did.''
Brock Nelson made it a one-goal game at 8:16 shortly after a power play, and Okposo tied it with 2:58 left on a lunging push with his stick after the puck struck his skate. The goal was confirmed by video replay.
Frans Nielsen and Tavares also scored in the four-round shootout against Ray Emery, who made 40 saves through overtime.
''We were in a good position and had opportunities,'' Emery said. ''I didn't stop the ones that I needed to stop. They gained momentum. We had them back on their heels, and they turned the tables.''
Anders Nilsson turned aside Vincent Lecavalier and Sean Couturier in the tiebreaker to help the Islanders avoid a four-game, season-series sweep. Philadelphia is 15-2-3 against New York since the start of the 2010-11 season.
''We created chances and found a way to make it count,'' Tavares said. ''It was meaningful as a group to come back with an effort like this after Saturday's game. Momentum is important for us.''
Matt Read did most of the offensive damage for the Flyers, netting two of Philadelphia's three goals in the second, and joining Claude Giroux with a goal in the shootout.
New York outshot Philadelphia 34-15 after the first, including 17-3 in the third, and scored twice on six power plays - tying it after Steve Downie was called for holding with 4:06 left.
''You can't win if you take penalties like we did,'' Flyers coach Craig Berube said. ''We got caught at the worst time.''
Read gave the Flyers a 1-0 lead with a short-handed goal and then stretched Philadelphia's advantage to 3-1 late in the second. Wayne Simmonds scored in between for the Flyers.
Read, who had an empty-netter in Saturday's win, has scored six of his 13 goals this season versus the Islanders. He has two two-goal games this season against New York and has 10 goals in 14 career games against the Islanders.
Nilsson made 26 saves through overtime as he subbed for Kevin Poulin, who gave up five goals on 31 shots Saturday at Philadelphia. Nilsson improved to 1-2-2 in his sixth outing of the season and 10th of his NHL career.
His only other career win was a shutout of New Jersey on March 4, 2012.
''It felt really good to be in there again,'' said Nilsson, who played in the NHL for the first time since Dec. 9 at Anaheim. ''Especially to get a big two points. I felt good with my angles. Felt strong.
''Of course, the comeback was great, and I found a way in the shootout.''
Emery beat the Islanders in relief of Steve Mason on Saturday, stopping all five shots he faced in 26 minutes.
Read got the scoring going 1:26 into the second, while teammate Nicklas Grossmann served a hooking penalty. Read raced with his puck from his zone, moved around defenseman Andrew MacDonald in front and scored with a backhander.
Tavares got the Islanders even at 9:26 when he jammed in a return pass from Okposo at the right post for his team-leading 23rd goal.
Simmonds put the Flyers back in front, scoring off his rebound at 11:30, and Read made it 3-1 with 1:44 left in the second. Philadelphia scored three times on nine second-period shots.
NOTES: Flyers RW Jakub Voracek injured his left hand and will be evaluated back in Philadelphia. ... The Islanders, who returned from a 4-2 trip, are 18-5-2 when they score at least three goals this season. ... Read played in his fourth game after missing six because of concussion symptoms. ... The Flyers are 15-2-4 when leading after two periods. ... New York D Travis Hamonic missed his fourth straight game (upper body).