Barzal skated around Kris Letang for a wrist shot on a short breakaway, cutting it to 5-1 at 10:47 of the second. It ended a 10-game goal drought for Barzal, and it was his first multipoint game since March 6.
"It's nice to score, but it wasn't a game-winner or a game breaker-goal," Barzal said. "It was nice to maybe get a little energy on the bench and pull Pittsburgh's lead] to four. As much as I'm trying to score, I'm trying to play the right way."
Anthony Beauvillier scored for a fourth straight game to make it 5-2 at 5:23 of the third period.
Jordan Eberle cut it to 5-3 on a snap shot at 17:33.
"You're just trying to get one in, and hopefully it snowballs," Eberle said. "That's what we were thinking."
Rust completed the hat trick with an empty-net goal with 42 seconds left for the 6-3 final. Each player on the Penguins' top line -- Rust, Crosby and Jake Guentzel -- has 14 goals this season.
"They lead the charge," Sullivan said. "I think they set the tone for the attitude of the team when we're going out to play every night. No one is looking for excuses. They all have the expectation that we are going to go out and win hockey games."
NOTES: The Penguins are 5-2-0 against the Islanders this season. … It was Rust's fourth NHL hat trick and first since he scored three goals against the Ottawa Senators on March 3, 2020. … Islanders forward Michael Dal Colle did not play because of a lower-body injury and is also out for the game Monday, Trotz said. Dal Colle was replaced by forward
[Kieffer Bellows
, who had two shots on goal in 11:54 of ice time. … Penguins forward Mark Jankowski did not play after entering the NHL COVID-19 protocol Saturday. … Islanders forward Josh Bailey had one assist in his 900th NHL game. He has scored 496 points (159 goals, 337 assists). … Crosby has scored 10 points (three goals, seven assists) in six games since center Evgeni Malkin sustained a lower-body injury March 16. Malkin is week to week.