Bunting had two of Arizona's season-high three power-play goals. Derick Brassard and Christian Dvorak also scored.
''I felt good,'' Bunting said. ''More and more games I get in, the more comfortable I can be with game, and I felt it tonight. The puck was on my stick and I was moving it well.''
Adin Hill made 36 saves to improve to 6-1-0 as a starter since Antti Raanta sustained a lower-body injury.
Drew Doughty had a power-play goal and Andreas Athanasiou also scored for the Kings, who have lost three straight. Cal Petersen made 28 saves.
Bunting completed his first hat trick 8:48 into the second period, tapping in the rebound of Jakob Chychrun's power-play shot.
''All these goals, every time I see 58 around the net, and he was not afraid to get in some people's faces,'' Coyotes coach Rick Tocchet said of Bunting.
Arizona was 3 for 6 on the power play. Los Angeles had allowed just one power-play goal in 31 chances over its previous 13 games.
Despite playing the second game of a back-to-back after beating Anaheim 3-2 in overtime on Sunday, the Coyotes blitzed the Kings with three goals in the opening 7:28. Bunting got them on the board with a one-timer in the slot 2:43 into the first, and he knocked in a power-play goal to make it 2-0 at 4:11.
''We just moved the puck quick and our power play was really clicking, and I was just trying to stay in front of the net and whack those in when I can,'' Bunting said.
Brassard made it 3-0 with another power-play goal on a one-timer set up by Conor Garland.
Doughty pulled the Kings within 3-1 at 16:07 on a long wrist shot that Hill couldn't see through traffic, but the veteran defenseman said the lack of intensity to start the game was too much to overcome.
''Compete. Act like you've earned your spot in this lineup and on our team and run with it. Don't sit around hoping you're going to get more shifts,'' Doughty said.
''Play as if it's a playoff series every single series we play in and that's it. I don't know what else to say,'' he added.
Athanasiou made it 4-2 at 2:10 of the third period.
Dvorak scored an empty-netter at 19:26.
Bunting had scored two goals in his first eight NHL games before matching that in the first period. It was the first multigoal and multipoint game for Bunting, a fourth-round draft pick in 2014. ''I think I've played over 300 games in the American League and I haven't even gotten a hat trick down there, and this is my first pro one so it's kind of funny how things work out,'' Bunting said.
Regarded as one of the most outspoken players in hockey, Doughty let loose after the Kings lost for the ninth time in their past 12 games. ''We've had some guys competing every single game, and we've had others take games on, play good games, and take games off. I mean, we're down 4-1 in the third period, I'd sure hope that we're playing a little more desperate, but it's absolutely ridiculous that we didn't play like that in the first or the second,'' he said.
Chychrun had two assists, giving him five points in back-to-back games against Anaheim and Los Angeles after getting his first hat trick against the Ducks. The five points are the most Chychrun has ever had in a two-game span.
Fellow defenseman Alex Goligoski also had two assists. He has six during a five-game streak.
The Coyotes and Kings play again in Los Angeles on Wednesday.
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