Ilya Samsonov allowed five goals on 20 shots before being pulled for the first time in his NHL career and replaced in the second period by Braden Holtby, who made 12 saves.
"It's always tough when it's your first time going through something like that," Holtby said. "The thing is, he had no chance -- it was just stacked against him. It's a big thing. He has a really good head on his shoulders, and I'm sure he knows that."
The Islanders took a 1-0 lead at 3:30 of the first period when Beauvillier scored on a 3-on-2 rush with a one-timer from the right circle off a pass from Bailey.
Beauvillier made it 2-0 at 6:16 when he scored off the rebound of a Nelson shot during a scramble in front.
"You kind of find your legs when you get points early," Beauvillier said, "and I thought we as a group just did a good job sticking with it and following the game plan, just doing the right things out there."
Beauvillier has five goals and three assists during a six-game point streak.
"I think he's just playing free and having fun and he's getting good looks," Nelson said. "He's got all the tools you need to play and be a great player in this league, and he's showing that."
Carlson scored with a shot from the point that went in off defenseman Johnny Boychuk at 12:55 to cut New York's lead to 2-1.
Defenseman Devon Toews made it 3-1 when he got behind the Washington defense to complete a give-and-go with Bailey at 18:06.
Leo Komorov pushed the lead to 4-1 with a wrist shot from the right face-off circle 45 seconds into the second period, and Jordan Eberle tapped in a pass from Anders Lee on the rush to make it 5-1 at 10:36, chasing Samsonov.
The Capitals, who came back from down 4-1 in the third period of a 6-4 win at the Islanders on Jan. 18, made it close, but their rally fell short.
Lars Eller put in the rebound of Carl Hagelin's wraparound at 11:25 to make it 5-2, and T.J. Oshie got Washington within 5-3 with a one-timer from the left circle on the power play at 16:59 of the second.
"A couple games lately we found ways to get back, and tonight I think we did a great job at trying to get back, but you know, ran out of time or the deficit was a little too big," Oshie said. "So we are struggling obviously a little bit, but you know, we can learn from a lot of these mistakes and grow and try to get better."
Capitals forward Evgeny Kuznetsov left the game at 9:14 of the second period with an upper-body injury after he was hit into the boards in front of the Islanders bench by Komarov. He's day to day.
