NEW YORK -- The Detroit Red Wings know all too well how it feels to lose to a struggling team that is playing the second game of a back-to-back set. On Sunday night, the Red Wings ensured the New York Islanders would experience that frustration, too.

Danny DeKeyser scored 1:02 into overtime Sunday night to cap a wild back-and-forth game and lift the Red Wings to a 4-3 win over the Islanders at Barclays Center.

The Red Wings squandered third period leads of 2-1 and 3-2 before squeaking out a victory in the second game of a three-game road trip. Detroit fell to the Pittsburgh Penguins, 5-3, on Saturday night.

"Especially coming off of last night, when they tied it up there in the third it was a tough feeling for us," DeKeyser said. "(But) we just kept playing."

The Red Wings improved to 2-1-1 in the second game of a back-to-back, though Sunday's win was the first time they've followed up a loss with a win. But they are accustomed to living life on the other side of the equation.

Overall this year, the Red Wings are just 1-4-0 against teams playing the second game of a back-to-back set, including 1-2-0 against teams that lost the night before. Detroit fell to the Florida Panthers on Oct. 30 and the Winnipeg Jets on Nov. 4 before beating the Dallas Stars on Nov. 29.

"We've lost some games (to) teams that came in and beat us when they were back-to-back and we were rested," Red Wings head coach Jeff Blashill said. "So we just understand we better take care of business the other way."

The Red Wings took care of business in roller coaster fashion Sunday, when the Islanders took a 1-0 lead on Anders Lee's goal just 5:16 into the first period. But Mike Green scored twice -- first with 7:07 left in the first and then with 5:20 remaining in the second -- to give Detroit a 2-1 lead heading into the third.

Islanders defenseman Johnny Boychuk tied the score 1:52 into the third, when he picked up a loose puck to the right of the faceoff circle and fired a shot past Red Wings goalie Petr Mrazek. The Red Wings seemingly retook the lead at the 6:32 mark, but Green's prospective third goal was overturned due to goalie interference by teammate Luke Glendening.

Henrik Zetterberg redirected a shot by Jonathan Ericsson with 6:54 remaining in regulation, but the Islanders tied it again when Josh Bailey poked home a loose puck in the crease with 4:21 to go.

"At that point, you're pushing, trying to get one," Bailey said. "We had to come back twice. That's how our group is, we're a resilient bunch. Just kept working, put our head down and keep going."

The Red Wings got the only two shots in overtime and won when Tomas Tatar streaked down the right side of the ice before passing to DeKeyser, who fired a shot over the glove of Islanders goalie Jaroslav Halak to end a two-game losing streak and give the Red Wings (12-11-3) their fourth victory in the last seven games (4-1-2).

"I like our mentality tonight," said Red Wings center Frans Nielsen, who had an assist in his first game against the Islanders, with whom he played his first 10 NHL seasons. "We got a goal disallowed, they came back twice but we didn't panic or anything. We just stuck with with it and played our game. I think it was a good game, a good road game for us."

Mrazek had 32 saves as the Red Wings moved within two points of the Washington Capitals and Boston Bruins, who are tied for the final wild card spot in the Eastern Conference.

Halak recorded 30 saves for the Islanders (9-10-5), who their three-game winning streak snapped. New York fell to 5-2-1 this season against teams playing the second game of a back-to-back set.

"Every point matters," Islanders center John Tavares said. "We really needed the two and tried to take advantage of a team on a tough back-to-back."

NOTES: Red Wings C Frans Nielsen, who played 606 games for the Islanders over 10 seasons before signing a six-year deal with the Red Wings in July, received a warm ovation during a tribute video that aired in the first period. "So many people (in) this organization mean so much to me," Nielsen said "It was awesome. I was happy about that." ... The Islanders scratched LW Anthony Beauvillier and G Thomas Greiss. ... Islanders G Jaroslav Halak, who made 38 saves in Thursday's 3-0 win over the Washington Capitals, started for the second straight game -- the first time he's started back-to-back games since he started seven straight from Nov. 3-18. ... The Red Wings scratched LW Tomas Nosek and D Ryan Sproul. ... Three injured Red Wings -- RW Andreas Athanasiou (knee), G Jimmy Howard (groin) and D Alexey Marchenko (shoulder) -- are skating with the team during its three-game road trip.