Sullivan has the most wins by a coach in Penguins history. He is 300-156-55 since being hired on Dec. 12, 2015.
"It's humbling. It means a lot", he said. "I'm grateful to the players. They're the guys that go out there and earn the wins for us. These guys that I've been coaching in my time here work so hard to bring the success that we've had on ice. I'm grateful to those guys. They're the ones that make the sacrifices every day."
Six different Pittsburgh players had a goal and Tristan Jarry made 39 saves as the Penguins (3-0-1) have outscored opponents 18-5 in three home games this season.
"I think I just want to get better every year", said Jarry, who has only allowed five goals on 104 shots in his three starts. "Every year, I want to take a step. Every year I come in, I'm a little bit more mature. I have a little more, I guess, games under me. So just being able to start, knowing what to expect, it does nothing but help."
Cal Petersen got the start in net for Los Angeles and allowed three goals on nine shots and was replaced by Jonathan Quick, who made 22 saves over the final two periods.
"I guess with Cal, there's no secret we have to get him going", said Kings coach Todd McLellan. "He has to play like he can play. He's an NHL goaltender. He's an outstanding young man that's played extremely well at this level. We're trying, just like we would with forwards and defenseman, to get him to where he can be. He has to be better."
Penguins get goals from six different players, pound Kings
Jan Ratta scored on Pittsburgh's first shot of the game, a snap shot past Petersen, who was screened by Jeff Zucker on the play.
Jake Guentzel made it 2-0 with 5:25 left in the first period, taking a pass from Kris Letang, who split the Kings defense, to tap it in.
He left the game after taking a shot from Letang up high at 6:51 of the third period and was being evaluated after the game, Sullivan said.
Ricard Rakell completed the scoring in the opening period as he went through the crease behind Petersen after a one-timer by Jeff Petry went off the left post.
"When I look at the start we had, I thought we played the way we wanted to play", McLellan said. "We played fast. We were aggressive, forced them into situations where they had to turn the puck over. Things were going pretty well for us. Even after the first goal, I thought we responded well. By the time it got to three, unfortunately, it wasn't the same way anymore."
Petry scored his first goal with Pittsburgh 4:13 into the second period on a wrist shot through traffic.
"To get the first one is a relief", he said. "I've had some looks, had some good shots. It's good to get that one under my belt."
Jeff Carter had a short breakaway and beat Quick five-hole to make it 5-0 and Ryan Poehling scored short-handed with a slap shot from the high slot.
Carl Grundstrom scored the lone goal for Los Angeles on a one-timer from the left face-off circle with 2:28 remaining on a power play.
"Being down 3-0 after the first period certainly doesn't help", said Kings forward Anze Kopitar. "I didn't think our play was that bad. Just a couple tough breaks. We're down 3-0 and then you're obviously playing catch up. You're trying to make something happen. It didn't happen tonight."