Kopitar, who is playing in his final NHL season, has 1,306 points (448 goals, 858 assists) 1,504 career games with the Kings. Dionne had 1,307 points (550 goals, 757 assists) in 921 games.
Trevor Moore and Adrian Kempe also scored for the Kings (27-23-15), who are 2-0-1 on a five-game road trip. Darcy Kuemper made 20 saves.
Emil Heineman scored twice, and Bo Horvat had two assists for the Islanders (37-24-5), who had won two in a row. Ilya Sorokin made 24 saves.
Moore gave the Kings a 1-0 lead at 3:33 of the first period. He blocked Scott Mayfield’s point shot before skating in on a breakaway and beating Sorokin over his blocker.
Kopitar extended the lead to 2-0 at 13:07. He tapped a slap pass from Mikey Anderson, who was at the left point, inside the right post.
Kempe made it 3-0 at 18:28 of the first. Artemi Panarin stole the puck from Matthew Schaefer in the neutral zone before finding a streaking Kempe, who redirected the pass with one hand on his stick over Sorokin’s glove.
Heineman cut the deficit to 3-1 at 10:46 of the second period, redirecting Adam Pelech’s point shot down off the ice in the slot.
Heineman then made it 3-2 at 3:38 of the third period when Schaefer’s point shot deflected in off his right knee in the low slot.
The Islanders had one last chance to tie it during a 6-on-4 after Scott Laughton was assessed two minor penalties with 3.1 seconds remaining. However, Schaefer’s shot following a face-off win by Jean-Gabriel Pageau was blocked by Joel Edmundson.
Prior to the face-off, Kings coach D.J. Smith called a timeout. In a 5-3 win against the Islanders on March 5, Bo Horvat had been able to beat the buzzer in the second period after a face-off win by Pageau with just one second remaining.