GLENDALE, Ariz. (AP) Jimmy Howard faced 35 shots Thursday night, the third time in three games Howard has seen at least that many attempts.
Howard stretched for a pad save on Clayton Keller's shot that looked like it would go under him, which started a short-handed rush that produced the tiebreaking goal for Luke Glendening with 3:24 to play.
''They threw it back door, so I was probably fortunate he (Keller) did a one-timer, because it allowed me to look it over and I was able to get a pad on it,'' Howard said. ''Good to see him (Glendening) get the game-winner.''
Dylan Larkin got the assist on Glendening's goal, his second of the night.
Frans Nielsen sent in a long empty-net goal with 1:34 to go to seal Detroit's third victory of the season. The Coyotes have one point through four games.
Keller scored twice for Arizona, with Max Domi assisting on both.
Louis Domingue came off the bench to make 21 saves for the Coyotes, forced to play when starter Antti Raanta had to leave after the first period with a lower-body injury. Domingue has played in three of the first four games of the season.
''It's not good. We're close but close is far from being good enough,'' Domingue said. ''It's a lot of self-searching. ... We've got to find a way to be more than close because not a win in four games to start the season, it's not good enough.''
Arizona had a 5-on-3 power play for 90 seconds in the first period, but the Red Wings survived that stretch and were 3 for 3 on the penalty kill in the first.
The Coyotes went 1 for 6 on power plays for the game.
Raanta, who gave up three goals in the first 6:15 of the Coyotes' 5-2 loss at Vegas on Tuesday night and was pulled from net, held the Red Wings scoreless on nine shots in the first period. He blocked a wide-open attempt from Nielsen with 4:19 to go.
Keller stuffed in a rebound off a shot from close range by Jordan Martinook at 6:12 of the second, giving the Coyotes a 1-0 lead and their first power-play goal since the season opener Oct. 5.
The Red Wings tied it at 1 on their fourth power-play goal of the season, scored by Frk on a long slap shot that got past Domingue's glove side at 11:37 of the second period. Mike Green got the assist, his fourth on a power play this season.
Frk has three goals in four games, and Green, with two assists, has eight on the season.
Keller's second goal made it 2-1 with 1:44 to play in the second. But Detroit answered, with Zetterberg tapping the puck between Domingue's legs after Larkin moved it around the boards behind the net.
Zetterberg's goal, his second of the season, came with 42 seconds to play in the period.
NOTES: Red Wings D Niklas Kronwall played his first game of the season after missing the first three with a groin injury. ... D Danny DeKeyser missed his first game of the season due to lower body injury suffered against Dallas on Tuesday. ... Keller recorded his first career multi-goal game, in just his seventh career NHL game ... Coyotes D Kevin Connauton (lower body) was scratched for the first time this season, with D Adam Clendening making his season debut. ... Martinook returned after missing Tuesday's game in Las Vegas with an injury.
Red Wings: Detroit travels to Las Vegas for its first meeting with the expansion Golden Knights on Friday night.
Coyotes: Host Boston on Saturday night.
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