Correction: An earlier version of this article incorrectly said that Capitals forward Mike Knuble hasn’t been to the third round of the NHL playoffs since 1998 with the Detroit Red Wings. He made the third round with the Philadelphia Flyers in 2008. This version has been corrected.

There’s a gleam in Coach Dale Hunter’s eyes whenever he talks about playing in a Game 7. These pressure cookers are the contests players remember most, he says, games with everything on the line where all that remains is to enjoy the ride and let instinct take over.

While his attitude reflected on each member of the Washington Capitals during a loose practice Friday as they prepared for one final game against the New York Rangers, it’s clear the gravity of the contest is not lost on them. A win Saturday night at Madison Square Garden would secure Washington’s first trip to the conference finals in 14 years.

“It’s the highest stakes you’re gonna play in. You’re playing for your life. You’re playing to continue to chase your dream,” versatile center Brooks Laich said.

Laich is part of the majority on the Capitals’ roster in that he has not advanced past the second round of the Stanley Cup playoffs. Mindful of the club’s early-round playoff failures in recent years, the Capitals don’t want this opportunity to pass them by.

“We’re desperate to get there,” Laich said. “You can’t keep saying every year, ‘Well we’ve got a good team and it will come.’ Eventually you have to push through and do it.”

Of the players who have suited up for Washington this postseason, only three have played in the conference finals — Mike Knuble, Troy Brouwer and Roman Hamrlik. New York is in a similar situation, with only four players — Brad Richards, Ruslan Fedotenko, Mike Rupp and backup goaltender Martin Biron — who have advanced to the third round.

Conventional wisdom suggests the Rangers face the greater burden of expectation heading into this meeting. They are the top-seeded team in the East, with home-ice advantage and a 4-0 record all-time in Game 7s at Madison Square Garden. The Capitals, meanwhile, are 3-7 in Game 7s all-time and 1-1 on the road.

This will mark the sixth time in the past five years that the Capitals’ core group of players has endured a seven-game series. The experiences haven’t been overwhelmingly positive (the team’s Game 7 record over that period is 2-3).

But the familiarity Alex Ovechkin, Nicklas Backstrom, Alexander Semin, Mike Green and Laich have with series-deciding games should be an asset.

“We know what to expect and I think that’s the key. We prepare the way we prepare, control what we control and we’ll be fine,” Green said. “You just got to go with your instincts.

“We’re so focused on our game plan and our system that everything should just come natural to us. And just play. Play with everything you have and don’t leave anything behind.”

Ovechkin was asked what he gleaned from those previous Game 7s and was equally matter-of-fact about the approach the Capitals must take.

“Most important thing, you have to take the best thing that you have and go out there and show what you have,” Ovechkin said. “Block shots, make hits, it doesn’t matter what’s going to happen, you just have to keep playing and keep focusing — be out there and do the best you can.”

For a team that was often inconsistent in the regular season, it’s a bit surprising that the Capitals’ greatest strength in the postseason stems from the commitment to their defensive-oriented system.

It’s helped them rebound from every tough loss and powered every victory throughout the playoffs.

It’s also what gives them confidence heading into one more elimination game as they try to erase the memory of four years of postseason disappointment and push Washington into the conference finals for the first time since 1998.

“It’s a big game and there’s no hiding from that fact, but I think when you feel confidence in the room and you can sense it from other guys, then you feel great about going out there,” said Knuble, who at 39 is playing in his 16th NHL campaign but has been to the third round only once since 1997-98 with Detroit. He knows how rare this opportunity is.

“You want guys to realize it doesn’t happen all the time like this,” Knuble said. “There’s five teams still involved in this thing. . . by [Saturday] night there’s going to be four teams left. You want to be one of those standing.”