The Red Wings held a 4-1 lead after two periods and held on to clip the Coyotes 5-3 at Little Caesars Arena.
Gustav Nyquist and Luke Glendening scored less than two-minutes apart in the first three-minutes of the first period.
Anthony Mantha and Dylan Larkin extended the lead in the second, and Darren Helm added an empty-netter in the third.
Jimmy Howard made 30 saves as the Red Wings improved to 6-6-and-1.
The Coyotes have lost 11-of-12 to start the season.