The Penguins were 15-14-3 on Dec. 19.
"There's always time's when you think it's going to be an uphill climb, but I don't think anyone expected to put as many together as we have here down the stretch but we worked hard and we've earned it," captain Sidney Crosby said.
The Islanders (42-26-9) fell to 9-2-1 in past 12 games at Barclays Center. They lead the Philadelphia Flyers, who defeated the Ottawa Senators on Saturday, by two points for the first wild card in the Eastern Conference.
"There's just no excuses for that effort," Islanders captain John Tavares said. "It's embarrassing, starting with myself. You have to look yourself in the mirror and ask how bad do you want [to make the playoffs]. It was a big game at an important time of the year and to play the way we did is unacceptable.
"We just came off of a decent stretch were we won four of five and had our backs up against the wall. It's another test on Monday [against the Tampa Bay Lightning], then into the last week. So it's up to us how bad we want it and where we want to get to. I believe in this group so it's just disappointing the way we played today."
New York was 0-for-5 on the power play, allowing a shorthanded goal, and killed one of three Penguins power plays.
"You're not going to win many games when you give up two power-play goals and a shorthanded goal," Islanders coach Jack Capuano said.