NEW YORK -- New York Rangers goaltender Henrik Lundqvist believes having a strong will to win usually leads to success in the Stanley Cup Playoffs.

He proved his point Wednesday in a 2-1 overtime victory against the Washington Capitals in Game 7 of the Eastern Conference Second Round series at Madison Square Garden. The win was New York's third straight against the Capitals after falling behind 3-1 in the best-of-7 series. The Rangers will play the Tampa Bay Lightning in Game 1 of the Eastern Conference Final at Madison Square Garden on Saturday (1 p.m. ET; NBC, CBC, TVA Sports).

Lundqvist made 35 saves on the way to winning his sixth straight Game 7, tying Martin Brodeur and Patrick Roy for the most career Game 7 victories in Stanley Cup history.

He was particularly brilliant in overtime, stopping eight shots before center Derek Stepan scored the winning goal at 11:24.

"I don't know if [overtime hockey] is good for you physically," Lundqvist said, tongue in cheek. "It probably shortens your life a little bit, but it's so intense and the heart rate is up, especially the way they came flying.

"It was hard for us to clear a couple of pucks but we battled hard."

Lundqvist has a history of success in Game 7s against the Capitals. He made 35 saves in a 5-0 victory in the deciding game of the 2013 Eastern Conference Quarterfinals, and 22 saves in a 2-1 win in Game 7 of the 2012 Eastern Conference Semifinals.

He allowed five goals on 110 shots in three straight wins against the Capitals to enable the Rangers to become the first team to rally from a 3-1 series deficit in consecutive years.

"A lot of these games come down to will and how badly you want it," Lundqvist said. "The teams are so even that it comes down to a battle in the corner, in front of the net or all over the ice. It's 1-on-1 battles against the opponent. If you want it bad enough, you have a good chance."

Lundqvist has proven how badly he wants it; he's won 14 of his past 17 elimination games dating to Game 6 of the 2012 Eastern Conference Quarterfinals against the Ottawa Senators. Lundqvist is 15-8 in 23 playoff games in which the Rangers have faced elimination, and he has won 10 straight elimination games at Madison Square Garden. In those games, he has a goals-against average of 0.96, two shutouts and a .968 save percentage.

"He was amazing," Rangers defenseman Keith Yandle said. "Every day he comes to work, he puts in his work and it shows on the ice how calm and confident and how good a player he is. He's so professional and he's a guy we can really rally around."

Lundqvist had to be extremely sharp at the start of overtime, when the Capitals produced four shots on goal in the opening four minutes while maintaining intense pressure in the Rangers' zone.

Lundqvist said he had a hunch beforehand that two goals would probably win the game.

"[Washington goaltender Braden] Holtby had been playing well and I felt the first two periods were more open, and then in the third it was two teams that knew the next goal was going to be huge," Lundqvist said. "It's just a good feeling to be part of this group. We've been through so many things over the last few years, so you appreciate these moments.

"It definitely helps that we've been part of so many things throughout the years, and in this situation we are confident in this group and how we play. In the end it all comes down to one play. It was close a couple times that they got the win [in other games]. But the puck was on our side, and it's just fun to get another chance."

Despite several tense moments throughout the series, and in Game 7 in particular, Lundqvist said he enjoyed himself.

"This series was fun; Washington played really well and Holtby was outstanding," he said. "Personally, it was a great challenge to try and stay in the game and try and match him by keeping the team in it when we needed it. It's fun when you feel like you are doing your part, and then there are moments when the team steps up and scores the big goals. You need each other to have success so it's a great feeling when you pull it off like this."

Rangers captain Ryan McDonagh, who finished Game 7 with one assist, five shots on goal in nine shot attempts, three takeaways and six blocked shots, felt the team stuck together when the Capitals pressed in the early stages of overtime.

"It was great that we kept them on the outskirts there and [Lundqvist] had to make a couple big saves, but in the end we knew we needed to get pucks towards the net," McDonagh said.

The Rangers are 9-5 all-time in Game 7s; they are 7-0 at Madison Square Garden.

"It's hard to describe," Lundqvist said when asked about the feeling of playing in a Game 7. "You try not to be ahead of yourself or anything like that, but it's hard not to. You know everything is on the line. It starts with confidence and that you can do it and take one game at a time, and we did a great job."

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