John Carlson scored, and Samsonov made 22 saves for the Capitals (20-7-4). Ovechkin's five-game goal streak ended.
"I thought as the game wore on, we started to generate more chances and more looks, we had lots of attempts," Washington coach Peter Laviolette said. "They did a good job of blocking shots, but we had zone time. We were doing a lot of things we wanted, just unable to get it done."
New York took a 1-0 lead at 17:49 of the first period off a face-off when Buchnevich went to the front of the net and redirected a centering pass from Adam Fox.
The Capitals tied it 1-1 when Carlson backhanded a loose puck past Kinkaid at 5:55 of the third period.
Brett Howden scored into an empty net with 28 seconds left for the 3-1 final.
The Rangers played their third game without coach David Quinn and assistants Jacques Martin, David Oliver and Greg Brown, who remain unavailable due to NHL COVID-19 protocol guidelines. Kris Knoblauch, coach of Hartford of the American Hockey League, filled in for Quinn.
"I was really worried about the confidence [after the Capitals tied it]," Knoblauch said. "It could have easily been, 'Oh, here we go again.' But the guys were positive, especially the leaders were talking and just wanted to make sure we finished this one out. I don't think there was panic at all."