Lee and Nelson each had two goals and an assist, and Ilya Sorokin made 40 saves for the Islanders (28-23-7), who ended a three-game skid (0-1-2) and moved into a tie with Pittsburgh for the two wild cards in the Eastern Conference. They visit the Boston Bruins on Saturday.
"We all look at the standings. We knew the importance going into the game," Parise said. "We have teams that are climbing behind us with games in hand and we have teams we're trying to catch. There's just not a lot of room for error for us right now."
Rickard Rakell scored twice, and Sidney Crosby had a goal and an assist for the Penguins (27-18-9), who host the New Jersey Devils on Saturday. Casey DeSmith made 23 saves.
The teams will play again in Pittsburgh on Monday.
"Obviously the results are important, especially at this time of year," Pittsburgh coach Mike Sullivan said. "So, we want to get results. I'm disappointed that we didn't get it because I thought we played well enough to, but that's hockey. We have to regroup. We have an important one tomorrow night. We have to get ready."