NEW YORK -- It was a goal literally years in the making, thanks to a shot Martin St. Louis works on day in day out.

"The goal he scored tonight is exactly what you see him practise every time he's on the ice," said Rangers coach Alain Vigneault. "Like 100 pucks, he's trying to put it right there."

On Sunday night, St. Louis' top-shelf snap shot from just below the faceoff dot was a dagger to the heart of the Canadiens.

The goal, which came at 6:02 of overtime, moved New York within one win of its first Stanley Cup final in 20 years with a 3-2 victory over the Montreal Canadiens. The win, which gave the Rangers a 3-1 lead in the Eastern Conference final, marked the first time the home side had triumphed in the series.

"I felt I had room (on the glove side), and I tried to trust what I saw, and obviously I've gone to that side quite a bit that last few games and he's made some good saves on me," St. Louis said of Habs goalie Dustin Tokarski. "Sometimes you just have to keep trusting what you see and I was fortunate to get it by him."

Said Tokarski: "I obviously gave him some room and he took advantage of it."

Game 5 is Tuesday night in Montreal, with the Rangers looking to put the Canadiens to the sword for a third straight game at the Bell Centre.

Carl Hagelin and Derick Brassard also scored for the Rangers, both on breakaways generated by stretch passes.

Francis Bouillon and P.K. Subban -- who played 33:16 on the night -- scored for Montreal.

The Rangers outshot the Canadiens 26-24 in regulation. Montreal had a 5-3 edge in overtime.

The Canadiens will fly home full of regrets, especially after coming back twice to force overtime. The Montreal power play was one-for-eight and yielded a Rangers short-handed goal.

"We had the opportunity on the power play and we didn't take advantage of it tonight," said coach Michel Therrien. "Yes, we scored a goal. It was a timely goal, but we gave up one and that was the (story) of the game. I thought our power play had to be better."

And Montreal's defensive play on the winning goal was shocking. The Canadiens had several chances to get the puck out of their defensive zone but couldn't do it. St. Louis had so much room he could have parked a Winnebago in the faceoff circle as tired defenders Andrei Markov and Alexei Emelin were caught on the wrong side of the play.

"Well, we got a few chances to get out of it and move the puck harder in our own end, and it cost us the game," lamented Therrien.

It was the third goal of the series for St. Louis, who attended the funeral of his mother between Games 1 and 2.

He was buzzing all night, leading the Rangers with five shots on goal in 21:01 of ice time. The goal was his first playoff overtime winner since Game 6 of the Stanley Cup final on June 5, 2004 at Calgary as a member of the Tampa Bay Lightning.

In a largely empty dressing room, the Canadiens looked for positives.

They will have a rabid home crowd -- the best in the world, according to goalie Tokarski -- at their back Tuesday as they look to stave off elimination.

"I don't think frustrated is the word," said Tokarski. "We had some chances, hit a post late and had a power play (in OT). It's a game of inches and we came short."

Said Montreal captain Brian Gionta: "I thought Tokarski played great for us, gave us a chance to win that game. We're not out of the series by any means."

History favours the Rangers, who are 12-1 in the 13 best-of-seven playoff series in which they led three games to one after Game 4.

Montreal is 2-16 when trailing 3-1 in a playoff series. The last time they overturned such a deficit was in 2009-10 against Washington.

But the Canadiens have already staved off elimination in these playoffs, reeling off two straight wins to defeat Boston four games to three in the previous round.

"This is far from over," said Rangers forward Brad Richards. "I remember sitting in here down 3-1 against Pittsburgh. They will feel bad tonight, but tomorrow they will wake up in front of their home crowd and once that game starts 3-1, you throw that out the window and it is back in the battle again.

"We have to realize the longer it goes the more life and more belief they get, so it's going to be a very important start to the next game."

Sunday's win came 20 years to the day that the Rangers defeated New Jersey 4-2 in Game 6 of the Eastern final. New York captain Mark Messier, who had guaranteed the win, scored a natural hat trick that night. The Rangers went on to beat Vancouver for the Cup.

Goalie Mike Richter and five other members of that championship team were in the stands Sunday.

New York was 0-for-3 with the man-advantage but scored shorthanded through Hagelin.

The Rangers took nine penalties -- including three straight in the third period and overtime -- to four for Montreal.

Vigneault did not dispute any of the calls.

"We put ourselves behind the 8-ball a few times by taking, I think it was five penalties 200 feet from our net. We're going to have to do a much better job than that," he said. "But give credit to our killers and our goaltender. They did a real good job."

After Subban tied it at 2-2 two minutes into the third, Montreal forward Alex Galchenyuk rang one off the goal post with a little over three minutes remaining. He thought he scored but play continued. Replays showed Lundqvist got his stick to the puck before it hit the crossbar and bounced down -- in front of the goal-line.

With New York's Derek Stepan recovering from a broken jaw suffered on a Brandon Prust hit in Game 3, Dominic Moore moved up to centre Rick Nash and Chris Kreider. Brassard returned from injury to centre Mats Zuccarello and Benoit Pouliot. J.T. Miller took the place of the suspended Dan Carcillo on the fourth line.

For Montreal, Michael Bournival stepped in for the suspended Prust on the fourth line and Bouillon replaced defenceman Nathan Beaulieu.

As in Game 3, Montreal found itself down 1-0 after a first period which could have been worse on the scoreboard.

New York came into the game not having allowed a power-play goal in its last eight games (22 times shorthanded). And the penalty kill produced offence.

The short-handed Rangers went ahead 12 seconds into a Pouliot penalty thanks to a Brian Boyle stretch pass from the blue-line. The speedy Hagelin broke in alone, faked a shot and tucked a backhand through the legs of Tokarski at 7:18 for his sixth of the playoffs.

Montreal's David Desharnais failed to corral a pass behind the New York goal and Ryan McDonagh poked the puck to Boyle to trigger the play.

It was the Rangers' first short-handed goal in 70 playoff games, dating back to April 9, 2008.

The penalty count was three to one against the Rangers by the 10-minute mark, but the Canadiens power play was sputtering.

Montreal began to push back after the goal and Brian Gionta had a glorious chance 12 minutes in on a Lundqvist rebound at the doorstep, but the puck bobbled and Lundqvist's pad was there when the Montreal captain finally got control.

Tokarski was buried by a sliding Nash five minutes into the second period but survived the collision. That prompted the officials to warn both benches about not crashing the crease.

The New York-born Bouillon tied it up with a blistering shot from the top of a circle on a two-on-one with Desharnais after a nifty Rene Bourque pass between his legs. Lundqvist got a piece of it with his shoulder, but the puck still went in top corner glove side at 8:08.

At times, the game was like table hockey with both sides looking to open up the other with long passes.

Tokarski robbed St. Louis on a breakaway late in the period, catching the puck with his glove as if it was spring-loaded.

The Rangers went ahead with 56 seconds remaining in the second when Dan Girardi found Brassard with a superb stretch pass from deep in his own end. Brassard raced in and unloaded a slapshot from the slot to beat Tokarski.

Lundqvist picked up an assist, the first by a Rangers goalie in the playoffs since Richter on May 11, 1997.

An early Montreal power play in the third -- its sixth man-advantage -- finally paid off when Subban hammered home a slapshot from the blue-line two minutes in.

It was Subban's first point of the series -- and first in six games -- but also his fifth goal of the playoffs.

Lundqvist recorded his 41st career playoff victory, tying him with Richter for first on the team's all-time playoff wins list.