Trevor Moore, Carl Grundstrom and Kevin Fiala also tallied goals for the Kings, who had dropped five of six coming into the game, including a crazy 9-8 overtime defeat against Seattle on Tuesday.
Jonathan Quick stopped 18 shots.
Kopitar gave the Kings their first lead 5:22 into the third period on a 4-on-4 situation. Kopitar skated the puck into the zone, deked J.J. Moser and beat Karel Vejmelka far side for his fourth goal in the last four games.
Los Angeles had a pair of power-play goals, marking the first time since March 2017 it has scored multiple times with the man advantage in three straight games.
Matias Maccelli had a goal and an assist for Arizona while Christian Fischer and Nick Bjugstad also scored. Patrik Nemeth had two assists.
Vejmelka made 27 saves as Arizona dropped to 4-5-2 on its 14-game road trip.
The Coyotes had a 3-1 lead eight minutes into the second period on goals by Maccelli and Bjugstad before the Kings rallied. Moore scored on the power play at 9:09 and Grundstrom evened it with 1:31 to go in the period with a snap shot from the faceoff circle that went between Vejmelka’s legs.