Kopitar, who is playing in his final NHL season, has 1,308 points (450 goals, 858 assists) in 1,505 career games with the Kings. Dionne had 1,307 points (550 goals, 757 assists) in 921 games.
Kopitar's second goal of the game on the power play, which set the record, came on a snap shot from low in the right face-off circle to pull the Kings into a 4-4 tie at 13:42 of the third period.
Jack Hughes then gave the Devils a 5-4 lead with a power-play goal on a one-timer from the right circle at 17:31. Timo Meier scored an empty-net goal at 19:52 for the 6-4 final.
Nico Hischier had two goals and two assists, and Arseny Gritsyuk had a goal and an assist, and Dougie Hamilton had two assists for the Devils (33-31-2), who had lost two straight and are 4-2-0 six games into a Devils record seven-game homestand. Jake Allen made 27 saves in his first start in eight games.
Artemi Panarin had a goal and two assists, and Brandt Clarke had three assists for the Kings (27-24-15), who are 2-1-1 on a five-game road trip. Anton Forsberg made 22 saves.
Cody Glass scored to give New Jersey a 1-0 lead at 7:58 of the first period on a snap shot from the left hash marks that deflected off Kopitar in the slot.
Hischier pushed it to 2-0 at 11:04 on a rebound at the left post.
Kopitar scored on the power play to cut it to 2-1 at 4:15 of the second period on a shot at the left post.
Panarin tied it 2-2 at 6:03 on a snap shot from the high slot. Panarin has 11 points (three goals, eight assists) in his first 10 games with the Kings, who acquired him in a
trade with the New York Rangers on Feb. 4.
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’s power-play goal gave New Jersey a 4-3 lead at 12:42 on a rebound from the slot.