"It's our mentality," Ovechkin said. "We lost one, we have to bounce back and bounce to a winning situation. We have an experienced group of guys here. We have good leadership and coaching staff who tell us we can't lose two in a row."
Forwards Mikhail Grabovski and Josh Bailey scored for the Islanders (26-17-6), and Jaroslav Halak made 20 saves in his first start since Jan. 25.
"One of the best games we've played in this building and still come away with no points," New York coach Jack Capuano said. "They got some timely scoring, and No. 8 (Ovechkin) was in a good spot."
Grabovski opened the scoring at 1:55 of the first period, tapping the rebound from Bailey's shot past a sprawling Holtby for his ninth goal.
Oshie tied it 1-1 at 7:28 of the first. Backstrom fed a spin-around pass to a streaking Oshie, who beat Halak with a slap shot from the slot for his 16th of the season.
"Including tonight, the last three games, our opponents have played like it's a playoff game, and we weren't really up to that speed," Oshie said. "I think tonight we caught up to it and I think everything else followed after that."
Burakovsky's 4-on-4 goal with 1:18 left in the second period gave the Capitals a 2-1 lead. Jason Chimera's shot ended up on the goal line, and Burakovsky tapped it in for his ninth goal.
When leading after two periods, the Capitals are an NHL-best 27-0-1.
Burakovsky, who has scored five goals in the past four games and is on a five-game point streak, has 12 points in 13 games since being promoted to Washington's second line. He said newfound confidence has played a part in his scoring streak.
"When I have confidence, everything is just flowing," Burakovsky said. "I just go with the flow. When you have a hard time, you're thinking more. When you have a lot of confidence, it's easier to do the right things. Right now, I think that's one part why I have so much success right now."