Garnet Hathaway, Tom Wilson and T.J. Oshie scored in regulation after the Capitals trailed 3-0 midway through the second period. Darcy Kuemper had 27 saves to help Washington snap a three-game losing streak and improve to 14-4-2 since Dec. 5.
Kuemper stopped Islanders forward Jean-Gabriel Pageau on a breakaway earlier in overtime before Orlov's heroics sealed the win and moved the Capitals four points ahead of the Islanders in the tightly packed Metropolitan Division.
''There was no time for panic down when we got down 3-0,'' said Kuemper, who improved to 13-11-4 this season. ''We started to take it to them physically and that helped turn the tide. Hopefully this is a win we can build off of.''
Sebastian Aho, Matt Martin and Hudson Fasching scored to help the Islanders build their lead early in the second period. Ilya Sorokin finished with 31 saves.
Aho opened the scoring at 4:24 of the first, blasting a shot from the point past Kuemper for his fourth goal of the season. Islander defensemen have 27 goals this season, tied with Carolina for the league lead.
Martin scored with 6:51 left in the period with his fourth and Fasching increased the lead to 3-0 at 3:51 of the second with his third.
Hathaway broke through for the Capitals with his seventh at 10:01 of the middle period. Alex Ovechkin had an assist on the play, extending his team lead to 50 points.
Wilson pulled the Capitals to 3-2 with his first goal this season with 6:52 left in the second. Wilson was playing only his fourth game following recovery from left knee surgery.
The Islanders were upset over the lack of a penalty call when Ovechkin hit Pageau from behind into the boards six-plus minutes into the second. Pageau was slow to get up but stayed in the game after he went to the Islanders locker room.
''Charging, boarding, whatever it might be. He took steps,'' Islanders coach Lane Lambert said. ''We should have been on the power play.''
The Islanders still held the slim lead entering the third and were 16-2-0 when leading through 40 minutes this season.
But the Capitals managed to score the only goal of the final period, sending the contest into overtime.
''The guys never quit,? Capitals coach Peter Laviolette said. ''We lost battles in the first but we started doing things right at the start of the second. To fight back and push, it was really good.''
Oshie tied it when his long shot from just inside the blueline at the left point eluded Sorokin at 5:54 of the third for Oshie's ninth of the season.
Oshie then set up Orlov for the winner in the final minute of overtime. Sonny Milano also assisted on the game-clinching goal which sparked a spirited celebration by the Capitals, who are 11-9-3 on the road.
''You're disappointed in how it finished,? Islanders defenseman Noah Dobson said. ''We got one point but you have to find a way to get both points. Unfortunately we didn't.''
The Islanders held a pregame moment of silence for Gino Odjick, the former forward who passed on Sunday at age 52. Odjick played 82 games for the Islanders over three seasons in the late 1990s.
Zach Parise played in his 127th consecutive game for the Islanders. The 38-year-old forward has played every game since joining the team in October 2021.
Capitals: Host Minnesota on Tuesday night.
Islanders: Host Boston on Wednesday night.
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