GLENDALE, Ariz. -- An exceptional save led to a breakaway short-handed goal and, in a matter of seconds, the Detroit Red Wings turned an indifferent performance for 57 minutes into a win -- and yet another disappointment for the Arizona Coyotes.

Luke Glendening scored short-handed with 3:24 remaining, and the Red Wings rode their penalty kill and timely scoring to defeat Arizona 4-2 on Thursday night and keep the Coyotes winless.

Seconds after goalie Jimmy Howard stuck out his pads to stop Coyotes rookie Clayton Keller's spin-a-rama shot -- denying Arizona the lead and Keller a hat trick -- Glendening finished off a two-on-one, short-handed break started by Dylan Larkin's up-ice rush by beating Louis Domingue with a wrist shot.

"Larks (Larkin) made a great play in the neutral zone to get by (Arizona center Max) Domi and made a great pass," Glendening said. "I just had my stick on the ice, I didn't do too much."

The decisive last few minutes were more than enough to do in Arizona (0-3-1). The Coyotes have led in three of their four losses this season yet still have only one point in the standings.

"I thought that was one of our better games, and we deserved better," Arizona coach Rick Tocchet said. "It's hard to win, and you've got to make the right decisions. We overplayed the two-on-one and it's in the net."

Frans Nielsen added an empty-net goal with 1:34 to play after Martin Frk and Henrik Zetterberg also scored for Detroit (3-1-0). Howard turned aside 33 shots.

"We did a great job on the PK (penalty kill). And the PK ended up getting us one (at the end)," Howard said.

Detroit killed off five of Arizona's six power plays and answered each of the 19-year-old Keller's two goals -- and, most important, kept him from getting his first NHL hat trick.

"You have to find a way," Coyotes center Derek Stepan said. "It's 2-2 with a few minutes left and (we've got) a power play. You've got to find a way to get it done. It's sounds ridiculous but it's the way it is. You can't play 57 minutes of a hockey game, you've got to play 60."

Arizona, which couldn't score during a five-on-three power play lasting 1:30 in the first, finally found the net on its fifth man advantage. Stepan dug the puck out of a scrum in front and pushed it toward the net, and Keller tapped it across the goal line 6:12 into the second.

"He's going to have a nice career if he can keep doing that," Stepan said of Keller, the No. 7 overall pick in the 2016 NHL Draft.

Frk responded with his third goal in four games, also on a power play, on a slap shot from the left point that Domingue couldn't stop.

Domingue (20 saves) came on at the start of second after starter Antti Raanta was lifted with a lower-body injury after stopping all nine shots he faced. Tocchet said it wasn't the same injury that kept Raanta out of the season opener a week ago.

Keller scored his third of the season with 1:44 left in the second, taking Domi's short pass and beating Howard with a wrist shot from the edge of the left circle.

"We were getting pucks deep and playing our style of game," Keller said. "I think if we do that, not that many teams can skate with us."

However, Zetterberg tied it with his second of the season with 42 seconds left in the period, putting a rebound of Larkin's bad-angle shot from along the goal line through Domingue's pads.

Larkin and Mike Green each had two assists for Detroit, and Domi had a pair of helpers for Arizona. Green has eight assists in four games this season.

"I've said it a lot but, in this league, special teams and goaltending are huge," Detroit coach Jeff Blashill said.

The Red Wings, 15-5-1 at Gila River Arena, play at expansion Vegas on Friday night.

NOTES: Red Wings D Niklas Kronwall made his season debut after missing the first three games with a groin injury. D Danny DeKeyser (lower body) was out. ... Coyotes D Adam Clendening was active for the first time this season. ... Arizona LW Jordan Martinook returned from a one-game layoff caused by a lower-body injury, but D Kevin Connauton (lower body), who scored Tuesday at Vegas, was out. ... No Coyotes player has a positive plus-minus rating after four games.