No team has accomplished the feat since. The Philadelphia Flyers, however, are a solid 60-minute effort away from changing that fact.
Just don't tell them.
"I think if you look at it like that, it seems daunting," Flyers coach Peter Laviolette said Friday morning at TD Garden, just hours before his team will face the Boston Bruins in Game 7 of this Eastern Conference Semifinal (7 p.m. ET, VERSUS, TSN, RDS, CSN-PH). "We have not focused about that. It's about winning games. We really methodically went very slowly. Here we are in Game 7 and the question still remains the same: Do we think we can beat the Boston Bruins tonight? There's a belief in our room that our team is a good hockey team and we can win."
"I feel like we're still here today because of what's in our room. Our team is in survival mode. We've been fighting. You don't win those fights unless there's the right type of people in the locker room."
-- Peter Laviolette
"It really is our fifth time that we've been faced with elimination," Laviolette said. "I feel like we're ready for this. The message hasn't changed from Day 1 since I've been here to where we are right now. Everything stays the same. The message is the same and what's expected is the same. It's important that we go out and we do what we've been doing."
Perhaps thinking about making history will deter the Flyers from the task at hand? Whatever the case may be, they're not interested in what the Islanders did 35 years ago.
"We're not really looking at any of that stuff … we're just looking at the game and focusing on playing the game to the best of our abilities," defenseman Chris Pronger said. "We've done a pretty good job over the last couple of months of really buying into what we need to do to be successful, no matter who's in the lineup."
It's a huge boon for the Flyers that Pronger is on their side. It's for reasons like Friday why Philadelphia General Manager Paul Holmgren acquired him at the Draft in June. Pronger won a Stanley Cup with the Anaheim Ducks in 2007, and in 2006 he lost a Game 7 with the Edmonton Oilers against Laviolette's Carolina Hurricanes in the Stanley Cup Final. One has to believe such a resume only can benefit the Flyers in Game 7.
"I think I have the experience having been in a number of them," Pronger said. "Veterans have been there before and they've been in situations like this and can be a calming influence. I add things like that to the table. At the end of the day, we have to go out there and play the game as well as we have the last three and hopefully get some of the bounces that we've gotten."
More importantly, they must continue to believe.
"I feel like we're still here today because of what's in our room," Laviolette said. "Our team is in survival mode. We've been fighting. You don't win those fights unless there's the right type of people in the locker room."
A victory Friday would propel Philadelphia's improbable run into the Eastern Conference Final. And thanks to a similar run by the eighth-seeded Montreal Canadiens, the Flyers -- the No. 7 seed in the conference -- would have home-ice advantage.
First things first, though. Philadelphia must defeat a Bruins team facing elimination for the first time this postseason.
"It's do-or-die … we've been in this position the last three games," Pronger said. "We've got to look at it the exact same way. The only difference is they're in the same position as we were the last three games. Both teams have their backs against the wall and we'll see who comes out on top."
Follow Brian Compton on Twitter: @BComptonNHL