Lucas Raymond scored for the Red Wings (33-27-6), who have lost all seven in regulation. Alex Lyon made 23 saves.
“This is as tough as it gets,” Detroit center David Perron said. “We’ve got to find a way to bounce back, and it has to happen Saturday against the (Buffalo) Sabres. We have to put our pride on the line and be better.”
Detroit has played the last five games without captain Dylan Larkin, who sustained a lower-body injury in a 4-0 loss to the Florida Panthers on March 2.
“We haven’t handled this well without Dylan,” Red Wings coach Derek Lalonde said. “There’s no reason for that. He’s a special, special player, and he’s our engine a lot of times, but we have very capable players.”
Cooley gave the Coyotes a 1-0 lead at 5:10 of the first period with a short-handed goal, beating Lyon five-hole with a backhand on a breakaway off a stretch pass from Dylan Guenther.
“They are growing and growing,” Bjugstad said of Cooley and Guenther. “They are going to be elite players in this league, and they are showing it at both ends of the ice.”
Raymond tied it 1-1 at 18:00 with a power-play goal, beating Ingram with a one-timer from the left circle off a cross-ice pass from Patrick Kane.
Carcone put the Coyotes back in front 2-1 at 8:36 of the second period when he redirected Alex Kerfoot’s shot from the high slot past Lyon.