Mitchell snapped a 2-2 tie with just his second goal of the season and first since Oct. 28 at Dallas. His slap shot from the top of the left circle sailed through traffic and found the top right corner of the net at 6:45.
It allowed the Kings to close their 10-game road trip with a 6-1-3 record, moving ahead of the Ducks in the tightly bunched Western Conference playoff race. The Kings are tied with Minnesota, Nashville and Calgary with 70 points each.
The Kings twice took one-goal leads only to watch the Ducks tie it up.
Goaltender Jonathan Quick made 25 saves for his 28th victory. Curtis McElhinney stopped 15 shots for the Ducks, who lost their fourth in a row.
Corey Perry's slap shot from near the blue line tied it 2-all for Anaheim at 10:05 of the penalty-free second. Perry's 31st goal was his sixth in the past eight games.
The Kings started the game slowly, with no shots on goal in the first 10:06. That's when Anaheim's Kyle Chipchura and the Kings' Kyle Clifford received five-minute fighting penalties, and the action was on.
Perhaps energized by the bout, Ryan Smyth scored to give the Kings a 1-0 lead at 12:13 of the first. His stick hit the rebound in mid-air off McElhinney's pad for his 20th goal.
Anaheim's Teemu Selanne notched his 20th goal 1:19 later, connecting with a slap shot from the left side near the blue line that tied the game. He has recorded points in eight of the past nine games.
The Kings regained a 2-1 lead when Anze Kopitar was perfectly positioned for a rebound that he sent in past McElhinney's left skate at 17:09.
Notes: Ducks captain Ryan Getzlaf missed the game to be with his wife, who gave birth to their nine-pound son, Ryder James Getzlaf, earlier Thursday. ... Selanne's goal was his 626th, putting him 14th on the career scoring list. ... The Kings improved to 45-36-18 all time against the Ducks. Los Angeles leads the season series 2-1 with three meetings left. ... Anaheim opened a season-long seven-game homestand. ... The Kings activated F Marco Sturm from injured reserve and he started the game. He missed the previous 13 games because of a lower body injury. ... The Ducks recalled G Ray Emery from the AHL's Syracuse Crunch and reassigned G Timo Pielmeier to the Crunch.