The Coyotes captain, out for three games with a back injury, scored the first and fourth goals of Phoenix's fourth victory in 14 games this season.
The scoring barrage led to the benching of both starting goalies, Phoenix's Curtis Joseph early in the first period and the Kings' Mathieu Garon early in the second.
Joseph's replacement, David LeNeveu, had 38 saves as the Kings outshot Phoenix 43-24.
The Coyotes, who entered averaging just over two goals per game, scored five straight goals to erase a 3-1 deficit and go up 6-3 in the second period.
Ed Jovanovski had a goal, assist and one spirited fight for the Coyotes.
Phoenix coach Wayne Gretzky pulled Joseph after the Kings scored twice in the first seven minutes, the first on a power-play goal by Anze Kopitar and second by Tom Kostopoulos that put the Kings up 2-1.
Derek Armstrong scored on Leneveu to make it 3-1. But the Coyotes came back with two goals in a 28-second span late in the first period.
Enver Lisin scored his first career goal, in his 10th NHL game, on a deflection of Zbynek Michalek's shot at 13:59, then Georges Laraque took a superb pass from Patrick Fischer and sent it past goalie Mathieu Garon at 14:27 of the first period to make it a 3-3 tie entering the second.
Phoenix scored twice early in the second, prompting Kings coach Marc Crawford to replace Garon with Dan Cloutier after Jovanovski's power-play goal made it 5-3 at 5:33 of the second.
The Coyotes, beaten by the Kings 4-0 in their first meeting of the season, promptly scored on Cloutier, too. Dennis Seidenberg's first goal of the season capped a run of five goals in a row to put Phoenix ahead 6-3 at 6:38 of the second period.
Los Angeles cut the lead to 6-4 at 17:34 of the second when Leneveu tried to cover the puck with his hands. But it popped free, and Alexander Frolov knocked it into the net.
Notes: Doan doubled his goal total for the season. ... Joseph was pulled after two periods of Phoenix's 6-2 loss at Anaheim on Friday. ... Kings defenceman Rob Blake appeared in his 1,000th NHL game. ... Coyotes C Mike Comrie injured a foot in the third period against Anaheim and didn't play.