Jason Zucker had a goal and an assist, and Tristan Jarry made 19 saves for the Penguins, the No. 1 seed. They have not advanced past the first round of the Stanley Cup Playoffs since 2018.
"I think it's just disappointment," Pittsburgh captain Sidney Crosby said. "It's not guaranteed to make the playoffs. We've been fortunate that we've been there a lot (15 straight seasons). Every time you get to play in the playoffs, it's an opportunity. It really is the best time of the year. You want to be in it. You want to play for a long time. You want to compete for the Stanley Cup, so it's never a good feeling when you lose."
Zucker gave Pittsburgh its third lead of the game on a redirection of Cody Ceci's shot at 1:53 of the second period to make it 3-2, but the Islanders responded with three goals in 2:59, including two in 13 seconds.
Nelson scored off a cross-ice feed from Josh Bailey to tie it 3-3 at 8:35, and Ryan Pulock scored on a one-timer at 8:48 to give New York a 4-3 lead.
Nelson scored again at 11:34 when his shot from the slot squeaked between Jarry's pads to make it 5-3, prompting the Penguins to call timeout.
"It was a crazy game, but never out of reach," Nelson said. "No quit in this team. We always try to fight back, and we were able to do that tonight."