Playing in front of a road crowd that was mostly contingent of Hockeytown faithful, Red Wings captain Dylan Larkin opened the scoring with a power-play goal at 8:34 of the second period. Arizona swiftly responded and leveled the game, 1-1, less than three minutes later in the same frame.
Pius Suter and David Perron scored 58 seconds apart early in the third to put Detroit ahead, 3-1. The Red Wings' sudden momentum didn't rattle the Coyotes, who rallied to force overtime and blanked Detroit in the shootout.
"I thought the effort was there," head coach Derek Lalonde said. "Obviously got tired there in the third and could have managed the 3-1 lead a bit better. But again, our effort tonight with three goals on the road should be enough to win."
Goalie Magnus Hellberg made 20 saves for the Red Wings in his first start since Jan. 7 at Toronto. Detroit (18-17-8; 44 points) earned a point on Tuesday, but is winless in its past three games. With the victory, Arizona (14-25-5; 33 points) snapped a nine-game skid.
"We know what's ahead of us," said Larkin, who became the first Red Wings skater to reach the 40-point mark this season. "And what we have to do."
NEXT UP: Detroit will conclude a three-game road trip out west on Thursday night, visiting the Vegas Golden Knights for a 10 p.m. ET/ 7 p.m. PT puck drop at T-Mobile Arena.