Brad Richards tied the game late in regulation and Marc Staal won it 1:35 into overtime as the Rangers snatched a 3-2 victory over the Capitals in Game 5 at Madison Square Garden.
Anton Stralman scored the other goal while Henrik Lundqvist made 16 stops for the Rangers, who now hold a 3-2 lead in this best-of-seven series and are a win away from advancing to the conference finals for the first time since 1997.
New York will have the chance to close out this series on Wednesday as Game 6 will take place in Washington.
Brooks Laich and John Carlson each scored for the Capitals, who will have to win the last two if they want to advance to the conference finals for the first time since 1998. Braden Holtby stopped 35 shots in the loss.
"We've been resilient all year so we have to come back home and play a hockey game," said Washington head coach Dale Hunter. "Everyone battled out there tonight and we just caught some bad breaks."
A double-minor penalty was assessed to Joel Ward after he caught Carl Hagelin with a high stick with 21.3 seconds to play and the Rangers pulled Lundqvist for a 6-on-4.
Michael Del Zotto sent a hard pass from the left point to the low left side where Ryan Callahan had a couple of swipes at it. Holtby made the stops, but Richards was able to jam it under the pad to tie the game with 6.6 seconds to play.
The Rangers then won the game while still on the power play in overtime as John Mitchell won a right circle draw back to Stall, who slid to his left then cranked a shot past that deflected off a Capital then a screened Holtby for the win.
"They're all emotional games," said New York head coach John Tortorella. "It's a kick in the gut when you lose because it happens so quickly and it's pretty exciting when you win because it happens quick."
The first goal of the game went to New York as a shot from the right boards by Stralman snuck past Holtby at the 10:44 mark of the first.
Lundqvist needed to make just four stops in the first to keep Washington off the board, but the Capitals finally broke through at the 8:15 mark of the second.
After a left circle faceoff win, the Caps controlled the puck in the New York end. Alex Ovechkin attempted a centering pass from the left boards, but it hit off the stick of a Ranger. It took a Washington bounce, though, and went to Laich, who fired a one-timer past the glove of Lundqvist for his second of the postseason.
The Caps then took the lead 4:20 into the third on a power play as Dennis Wideman sent a pass from the right point to the slot where Carlson's one-timer snuck past the glove of Lundqvist.
New York went 2-for-4 on the power play while Washington was 1- for-4...Richards has five goals in the playoffs...This is the seventh playoff series between these two teams. Washington has taken four of them...Troy Brouwer had two assists for the Capitals.