Kevin Fiala had a goal and an assist, and Jonathan Quick made 18 saves for the Kings (13-9-4), who extended their point streak to four games (2-0-2).
"I don't know about a statement game, but I thought our energy was there right off the start," said Kopitar, the Los Angeles captain. "It was a bit of a test in the second period where you go down two goals, and we came back."
Matias Maccelli had a goal and an assist, Christian Fischer scored short-handed, and Dylan Guenther had two assists for the Coyotes (7-11-3), who have lost three in a row (0-2-1). Karel Vejmelka made 27 saves.
"It's frustrating when you don't make the simple play and turn it over," Fischer said. "That's when they come and they score and they win. Just have to tighten up defensively."
Kopitar's second goal of the game gave the Kings a 4-3 lead at 5:22 of the third period. He skated in along the right boards to get behind three defenders before scoring on a wrist shot from the right face-off circle during a 4-on-4 situation. He has five points (four goals, one assist) in his past four games.
"I've been feeling pretty well the past few games." Kopitar said. "I thought our line (Kopitar, Fiala, Adrian Kempe) throughout the last four, five, six games, we've been creating quite a few chances, just maybe not necessarily cashing in on a whole lot of them. But tonight, it kind of opened up and we're going to need more of the same going forward."