DETROIT -- The Detroit Red Wings could have earned a few days’ rest and saved the wear and tear of having to make a third trip West in a two-week span.

But they couldn’t take care of business at home in Game 6 of the Western Conference quarterfinals. Now, they’re dangerously close to getting an extended break.

The Red Wings squandered an opportunity Sunday afternoon to finish off the Phoenix Coyotes, getting dominated on special teams and losing 5-2 at Joe Louis Arena.

With the series tied 3-3, the teams will play a winner-take-all Game 7 on Tuesday at Jobing.com Arena.

The Red Wings are confident and defiant heading into their first opening-round Game 7 since 1994.

“We’ll be just fine. I have no doubt about that,’’ Detroit defenseman Niklas Kronwall said. “We’ve been in this situation before where we had a chance to close it out. But it didn’t happen tonight, and now, we’re going to go down and do it in Phoenix instead.’’

Each club has won two of three games on the road in this series.

“They’re a good team, but we think we’re a better team,’’ Red Wings coach Mike Babcock said. “The better team advances, pure and simple. We have an opportunity to play in a Game 7. We have to embrace that and come out and play.’’

Phoenix scored three times on the power play after failing to convert on its previous 19 opportunities and got the ball rolling with a short-handed goal. The Red Wings went 0-for-5 on the power play.

“They won the special teams battle, and that sucked the life out of our team,’’ Babcock said.

COYOTES 5, RED WINGS 2 Key play: Radim Vrbata converted a good pass by Robert Lang from the half-wall on the power play, giving Phoenix a 3-1 lead after Detroit had gained some momentum on a goal by Brad Stuart.



Hero: Coyotes goaltender Ilya Bryzgalov had his best game of the series with 31 saves, including some huge stops during three consecutive Red Wings power plays early in the first period.



Goat: Henrik Zetterberg, the best player through five games, had a rough day. He had no points, only two shots on goal, a minus-2 rating and lost a defensive-zone faceoff that led to Wojtek Wolski’s goal that made it 4-1.



Analysis: The Red Wings overcame a lot of adversity during an injury-plagued regular season, but this is their biggest challenge. After losing the special teams battle and squandering a chance to end the series, Detroit must regroup mentally from the disappointment and physically from another taxing trip out West for Game 7. The top two lines must deliver the kind of energy the bottom-six forwards have shown the past couple games.

Coyotes goaltender Ilya Bryzgalov played his finest game of the series. He made 31 saves, including several big stops during three consecutive Detroit power plays -- including a two-man advantage for 1:09 -- within the first seven minutes of the game.

“That’s probably the game right there,’’ Red Wings forward Henrik Zetterberg said. “If we would have scored on one or two of those chances, the outcome probably would’ve been a little different.’’

To make matters worse, Lauri Korpikoski scored a short-handed goal at 4:10 to put Phoenix ahead. He stripped the puck from Brad Stuart in the neutral zone, skated down the left wing and fired a shot through Jimmy Howard’s legs.

“I just tried to make a play, they closed it off and got a break,’’ Stuart said. “My fault.’’

Leading 2-1, the Coyotes scored twice in a span of 4:59 in the second period to break it open.

Radim Vrbata scored on the power play at 10:09, converting a cross-ice pass from the half-wall by former Red Wing Robert Lang. Wojtek Wolski added an even-strength goal at 14:01 by standing in front of the net and having Petr Prucha’s shot deflect in off him.

Any hopes of a stirring third-period comeback were quashed when Taylor Pyatt deflected in a shot by Keith Yandle on the power play at 5:25 to make it 5-1.

“You want to do a better job in front of (Howard), being in lanes and helping out,’’ Red Wings captain Nicklas Lidstrom said. “They were creating a lot of traffic in front of him. That’s what happens when you have a lot of bodies in front of the net and you get your shots through.’’

On the flip side, Lidstrom said of his team’s power play, which is 0-for-11 in the past two games: “(Bryzgalov) was making the first save and they were doing a good job clearing the rebounds and getting the puck out of there in front of him. You got to continue to shoot the puck. You can’t get discouraged when he’s making saves.’’

Stuart scored Detroit’s first goal on a screened shot from the slot at 2:51 of the second period. It came 24 seconds after former Red Wing Mathieu Schneider scored on the power play to put Phoenix ahead 2-0.

But the Red Wings were unable to build any momentum off Stuart’s goal, getting only a late goal from Darren Helm when the game was out of reach.

The Coyotes played without captain Shane Doan, a power forward who hasn’t returned since suffering an apparent right shoulder injury two minutes into the second period of Game 3. But it didn’t matter.

Now, the Red Wings are faced with having to win a Game 7 on the road, something they haven’t done since the 1964 semifinals against the Chicago Blackhawks.

“No question about it, when you have anybody down you want to get rid of them,’’ Babcock said. “The only disappointment I had is that we didn’t win. I liked our preparation. I liked our attitude.

“Everyone is upset and disappointed right now, but we’re going to shake this off.’’