The Kings scored all of their goals on the power play and Phoenix was assessed 57 penalty minutes.
Backup goaltender Mathieu Garon earned his ninth career shutout for the Kings, who snapped a four-game losing streak.
Phoenix, last in the Western Conference, lost for the fifth time in six games.
Phoenix backup goalie Mike Morrison allowed three goals on 13 shots in a painful home debut as a Coyote.
Sharks 5, Red Wings 1
At San Jose, California, Patrick Marleau scored two of San Jose's five power-play goals and the Sharks rolled to the best start in franchise history with their sixth victory in seven games.
Milan Michalek, Mark Bell and Marleau scored in the first 15 minutes to chase Detroit goalie Chris Osgood.
Jonathan Cheechoo and Marleau added third-period goals as the Sharks tied their club record for power-play scores, set last February against Detroit.
Vesa Toskala made 21 saves to remain unbeaten this season.
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