Daniel Sprong scored his third goal in two games for the Capitals (32-13-4), who swept the three-game set and have won seven of nine.
"We're playing well. It's a good time of year to be hitting our stride," Washington forward Tom Wilson said. "I think guys are feeling comfortable with the system. I think we were feeling comfortable with the system earlier on, but there was still a little bit of hesitancy. Now I just feel like it's a little smoother."
The Capitals, who played their second straight game without injured forward Alex Ovechkin (lower body), won 1-0 in a shootout last Thursday and 6-3 on Saturday, each at New York. They won six of eight games against the Islanders this season.
Ilya Sorokin made 32 saves for the Islanders (29-15-5), who have lost five of seven and have scored 15 goals (two in overtime) in their past nine games.
"A 1-0 loss against a very good team's not what you want," New York coach Barry Trotz said, "but it's not coming real easy right now, and a lot of that's due to a little bit on our part and a little bit on the competition as well."
Washington is one point ahead of the second-place Pittsburgh Penguins in the eight-team East; the Penguins lost 3-1 to the Boston Bruins on Tuesday. The Islanders are third, one point ahead of the Bruins. The top four teams qualify for the playoffs.
Vanecek, a rookie, got his second shutout after he allowed nine goals over his previous two starts.
"It wasn't too many shots, but you try and stay focused all game and try and help the teammates [by making] a save," Vanecek said. "They helped me a lot. That's why they didn't shoot too many shots."