Hischier pushed it to 2-0 at 11:04 on a rebound at the left post.
Kopitar’s first power-play goal cut it to 2-1 at 4:15 of the second period on a shot at the left post.
"Anze's just so responsible, so even keel," Clarke said. "I mean, when someone's down, he's there to pick you up. If you need to know what to do, you kind of look at him and just his poise and just the way he carries himself. He's just a true leader on and off the ice and, like I've said many times before, we're just super grateful to have him."
Panarin tied it 2-2 at 6:03 on a snap shot from the high slot.
Taylor Ward gave Los Angeles a 3-2 lead at 11:43 on a slap shot from the top of the left face-off circle.
Gritsyuk pulled the Devils into a 3-3 tie 25 seconds into the third period when he finished a 2-on-1 with Lenni Hameenaho.
Hischier scored on the power play to give New Jersey a 4-3 lead at 12:42 on a rebound from the slot.
The Devils lined up to congratulate Kopitar at the end of the game, as the New York Islanders did after Los Angeles’ 3-2 road win on Friday.
"It's a lot easier to do after a win than after a loss, but I appreciate all the battles that we've gone through with the guys, whether it was with New Jersey or another team," Kopitar said. "I guess it's been an honor, obviously. It's always nice to see that the guys want to do it."
NOTES: Panarin has 12 points (three goals, nine assists) in his first 10 games with the Kings, who acquired him in a trade with the New York Rangers on Feb. 4. ... Kopitar has seven points (four goals, three assists) in his past seven games. ... Hischier tied Zach Parise (194) for the fifth-most goals in Devils/Kansas City Scouts/Colorado Rockies history.