Adam Fox scored twice, and Jonathan Quick made 18 saves for the Rangers (26-13-2), who have lost four straight (0-3-1) and five of six in January (1-4-1).
"This one's a little bit different for me," New York coach Peter Laviolette said. "I thought we were, for the most part, pretty tight defensively. They had two chances in the third. They threw two pucks from the side of the net, and they ended up in.
"The previous games, we generated just a ton of offense and just gave up a little bit too much. They're different. But it doesn't matter. We've got to win a game tomorrow, and that's the bottom line."
The Rangers and Capitals will play again at Madison Square Garden in New York on Sunday (1 p.m. ET; MNMT, NHLN, MSG, SN).
"Just keep playing through it. It's a long season," Rangers captain Jacob Trouba said. "We're not playing terrible hockey. We're getting good looks. We're giving up a little too much, I think, the quality of chances. We know that, but we're going to keep battling through it. It is what it is."
Fox put the Rangers in front 1-0 at 13:23 of the first period. He attempted a centering pass to Mika Zibanejad that went back to him off the skate of Washington defenseman Nick Jensen. Fox then shot into an open left side of the net with Lindgren out of position.