Charlie Lindgren made 32 saves for the Capitals (51-21-9), who had lost two in a row (outscored 11-1).
Washington, which will finish first in the Metropolitan Division, will conclude its regular season at the Pittsburgh Penguins on Thursday.
“I thought it was a good win,” Lindgren said. “I thought it was a really good team win. I felt like it was one of the cleaner games we've played in a while. I thought from start to finish it was just a consistent effort. I thought we did a lot of really good things offensively. I thought defensively we were steady tonight and detailed. We didn't turn the puck over and, yeah, credit to our guys. I mean, I think we needed that effort in Game 81, you know? It just makes us feel better about our game.”
Jean-Gabriel Pageau scored for the Islanders (35-34-12), who have lost four of their past five games (1-2-2). Ilya Sorokin made 33 saves.
New York, which has been eliminated from playoff contention, will conclude its regular season at the Columbus Blue Jackets on Thursday.
“We're going to play till the end,” Islanders coach Patrick Roy said. “We’re not going to give up. I know we put ourselves in that position. We're not in the playoffs, and we're all disappointed, but we're going to play. ... Everybody wanted to play, and I thought that the guys, I mean, give everything they had.”
Strome gave the Capitals a 1-0 lead on a power play at 8:15 of the first period. He scored with a point shot that deflected off Islanders defenseman Ryan Pulock and beat Sorokin blocker side.
Strome extended the lead to 2-0 at 7:52 of the second period. Ovechkin stole the puck from Scott Mayfield behind the net and sent a backhand pass to Strome, who scored with a shot from the high slot that snuck under Sorokin's blocker arm.
Anders Lee appeared to score for the Islanders on a power play at 1:19 of the third period, but the goal was waved off immediately. Lee had tried to catch the puck in the low slot but ended up knocking it into the net with his glove instead.
Pageau did cut the lead to 2-1 at 11:36 of the third, knocking in Hudson Fasching's centering pass at the top of the crease.