Mike Zigomanis had two goals and an assist for the Coyotes, who have won three of four. Oleg Saprykin, Patrick Fischer and Zbynek Michalek each had a goal and an assist. Shane Doan added a goal as well.
Nagy was back in the lineup after being benched by Phoenix coach Wayne Gretzky for the third period of Phoenix's 4-0 loss to Minnesota on Friday. Nagy then was a healthy scratch Saturday for the Coyotes' 2-1 win in St. Louis.
Derek Armstrong had two goals and an assist for the Kings, who had won two straight. Michael Cammalleri and Craig Conroy also scored for Los Angeles.
Fischer broke a 3-3 tie at 17:59 of the first period, beating reserve goalie Barry Brust on a long rebound from the low slot off Nagy's shot.
Conroy tied the game 39 seconds earlier with a power-play goal from the bottom of the right circle.
Doan extended the Coyotes' lead to 5-3 on a power-play goal 55 seconds into the third period, blasting a shot from beyond the top of the left circle over Brust's glove. Armstrong made it 5-4 at 7:33 of the second when he took a pass from Tom Kostopoulos in front of the net, faked Curtis Joseph to the ice and scored into the open top half of the net.
Zigomanis put Phoenix ahead 6-4 with 8:46 remaining on a wrist shot from the left boards. Zigomanis added his second with 4:06 to go, redirecting Michalek's drive over a ducking Brust.