The Capitals took a 3-1 lead in the Eastern Conference quarterfinals and will try to close out the series at home Saturday.
It was a brutal loss for the Rangers, who took a 3-0 lead into the third period before Washington finally solved goaltender Henrik Lundqvist.
Lundqvist then made the miscue that led to the winning goal. He stopped a shot from the right circle by Marcus Johansson, but the attempt was partially blocked and it rolled toward Lundqvist.
He chose to simply bat the puck away with his stick, but it hopped straight to Chimera. It hit Chimera in the chest and bounced across the goal line.
Lundqvist finished with 49 saves.
Alexander Semin began the Washington comeback 2:47 into the third and Marcus Johansson then scored his first two goals of the playoffs to tie it. Johansson's second goal came with 7:53 to go in regulation.
Michael Neuvirth stopped 36 shots for the Capitals.
New York's goals all came in the second period from Artem Anisimov, Marian Gaborik and Brandon Dubinsky. The last two goals were scored just 7 seconds apart.