Alex Iafallo scored two goals, and Jonathan Quick made 32 saves for the Kings (9-8-4), who are 1-3-3 in their past seven games.
"Our quality or level of play hasn't fallen off dramatically. We haven't got the results," Los Angeles coach Todd McLellan said. "Timely goals … timely defensive plays, maybe one on the power play would have helped somewhere along the line. But you got to find a way to get past close, and that's where we are right now."
Kings defenseman Drew Doughty had an assist and played a game-high 27:55 in his return after missing 16 games because of a knee contusion. He was injured on a knee-on-knee collision with defenseman Jani Hakanpää during a 3-2 overtime loss at the Dallas Stars on Oct. 22, and was originally expected to miss 6-8 weeks.
"After two shifts, I realized I still got it," Doughty said. "But I was a little worried before my first couple shifts, not going to lie. I haven't been nervous before a hockey game probably since my first NHL game, and tonight I kind of felt it."
Adrian Kempe brought the Kings within 4-2 at 7:56 of the third, redirecting Matt Roy's shot from the blue line.
Los Angeles looked to have made it 4-3 at 8:17, but a video review determined Carl Grundstrom used a high stick to knock down Sean Durzi's shot from the blue line before putting it in.
Iafallo and Dustin Brown then scored 26 seconds apart to tie the game. Iafallo tipped Doughty's shot to cut it to 4-3 at 15:08, and Brown put in his own rebound from close range to tie it 4-4 at 15:34.
"Things happen on the ice," Anaheim coach Dallas Eakins said. "If the other team gets close, they tie it up, they get within a goal, well, now you've got a choice to make. You can either get ready for your next shift, be ready for the next moment and be ready to go, or you can sit there and hang your head on the bench and be left in the past moments, and you're just going to get crushed. Our guys have been unbelievably resilient and excellent in those situations."