The Capitals scored first, but a New York goal in regulation tied it and another in overtime sent Washington home.
Despite a valiant comeback spurred by third-period goals from Evgeny Kuznetsov and Joel Ward, the Capitals could not survive a slow start. They'll play Game 7 Wednesday in New York.
The Caps came within 1:41 of advancing, but the Rangers earned themselves one more game with a late goal and the overtime win.
Behind two goals from rookie Andre Burakovsky, Washington topped New York in Game 4 to move within one win of the Eastern Conference Finals.