Jamie McGinn lit the lamp twice as the Coyotes clipped the Red Wings 4-1 at Joe Louis Arena.
Mike Smith stopped 37 of the 38 shots he faced in the winning effort as Arizona won for only the second time in the last eight games.
Andreas Athanasiou scored the lone Detroit goal in defeat as Detroit remains one of the lowest scoring teams in the NHL.
Jimmy Howard had a rough night, giving up four goals on 18 shots, as the Red Wings dropped their third straight contest.