Boyd Gordon netted an unassisted, shorthanded goal 7:22 into the first period after Martin Hanzel was sent to the penalty box for two minutes for tripping Darren Helm. Gordon beat Red Wings goalie Joey McDonald on a breakaway after a bit of confusion from Ian White and Niklas Kronwall.
Meanwhile, Coyotes goalie Mike Smith has stopped all six shots from Detroit so far.
Detroit is coming off its first shootout loss of the season, and they are aiming to come back home with three wins in the five-game road trip.
The Red Wings won the first three matchups with the Coyotes this season.