DETROIT -- The Detroit Red Wings didn't have their legs. But they picked up the victory anyway.

scored the winning goal in overtime Monday night as the Red Wings returned from a three-game grind through western Canada with a 3-2 win against the Phoenix Coyotes.

"I think it's real good for the guys," Red Wings coach

said. "It's a real gut-check thing. Mental toughness is just, in the end, making the decision that you're going to get it done even if your legs don't move. I thought that's what the guys did."

The Red Wings returned home from a three-game road trip through Calgary, Edmonton and Vancouver with a flight in the early hours Sunday and didn't have much time to get their legs back before facing the Coyotes, the only team to beat Detroit at home in regulation this season.

But they got the job done in their first game back.

"Guys came out and worked as hard as they possibly could," Babcock said. "Lots of times, it wasn't pretty. We were playing on fumes, but they'll get a good day off tomorrow. They should be proud. It was a tough game to win coming back."

Zetterberg was not the least bit surprised that it was a struggle.

"You know you won't have your legs," he said. "That's the thing. You've just got to go out and play simple and not play back-and-forth hockey. If you do that, you have no chance."

The Red Wings had an extra attacker on the ice when they scored the winning goal because of a delayed penalty call against the Coyotes.

came off the bench, took a pass from Zetterberg and fired a cross-ice pass to Ruslan Salei. Salei let loose with a shot from the point, and Zetterberg deflected it in for the game winner.

"(Bertuzzi) made a good pass to (Salei) and he really held on to the puck, so I had a chance to get to the side of the net," Zetterberg said. "He made a good shot pass and I just put the stick there, and it went in."

Both teams played late-night games out West on Saturday, so both were battling the same fatigue. Babcock shuffled the lines up throughout the game looking for good combinations, and the puck took some interesting bounces.

Both goals in the first period -- one by Red Wings forward

and the other by Coyotes center Martin Hanzel -- came on hard bounces off the boards behind the net.

Nicklas Lidstrom also scored for the Red Wings, extending his streak of consecutive games with a point to nine. His goal about 7 1/2 minutes into the third period tied the score at 2-2 and set up the winner by Zetterberg.

The Red Wings will have plenty of time to get their legs back. They will take the day off from practice Tuesday and will not hit the road again until Nov. 24, when they travel to Atlanta to play the Thrashers.

Monday's action was the first of a six-game homestand for the Red Wings.

"We knew it wasn't going to be a beautiful win if we were going to get the 'W,' " Zetterberg said. "It was a pretty ugly one, but we're taking it. We're happy to get the win and have the day off tomorrow."

Someone joked with Zetterberg that Babcock had called for a surprise practice Tuesday.

"It's just going to be the coaches then," Zetterberg said, smiling.