DALLAS -- Detroit Red Wings coach Mike Babcock thought his team was set up to fail, having to play three road games in four nights after the Christmas break with a depleted lineup.

Much to his surprise, the tough trip was a rousing success.

The Red Wings scored six unanswered goals to battle back from a two-goal deficit and defeated the Dallas Stars 7-3 at American Airlines Center for their third consecutive victory.

Patrick Eaves notched his first career hat trick and added an assist. The Red Wings scored four goals in the third period to snap a 3-3 tie.

“A trip like this after Christmas, back-to-back to start out, you’re set up to fail,’’ Babcock said. “Our guys found a way to get it done. (Dallas) played last night, that helped us as well. But still, you could easily go on this trip and end up 0-3.’’

It was Detroit’s first win in Dallas in seven games (1-4-2).

Nicklas Lidstrom and Jiri Hudler each had a goal and an assist. Brad Stuart and Kris Draper also scored goals. Todd Bertuzzi and Johan Franzen each had a pair of assists. And Jimmy Howard made 28 saves to raise his record to 20-6-2.

“We showed a lot of character by the way we played on this trip,’’ Red Wings captain Nicklas Lidstrom said. “We responded really well to the third game in four nights on the road. It’s great to see, especially with key people being out of the lineup.’’

After losing Pavel Datsyuk and Danny Cleary to injuries in the last week, the Red Wings need more contribution from other players. Eaves, a fourth-line grinder and penalty killer, is seizing the opportunity.

He scored his first power-play goal since March 3, 2009, when he played for Carolina, to tie the game at 3-3 at 17:38 of the second period. With his team leading 5-3, Eaves added a couple of insurance goals in the third, at 14:07 and at 17:46, shorthanded, into an empty net.

“That was awesome,’’ Eaves said. “There were some pretty special passes coming my way. I was finding some open spots and they went in. I’ll take all of them. It was a huge win for us. We responded after being down 3-1. It was a good road trip for us.’’

Eaves earned some shifts with Henrik Zetterberg and Johan Franzen and responded. He has 11 goals.

“It’s great to see,’’ Lidstrom said. “He’s got a great shot, he finds that open spot and knows where to go. He got rewarded by shooting the puck and finding his open spots.’’

Stuart snapped a 3-3 tie, giving his team the lead for good, at 5:29 of the third period. Stuart scored on a blast from just inside the blue line. Drew Miller worked down low to get the puck to Hudler at the point. Hudler passed to Stuart and Justin Abdelkader screened goaltender Kari Lehtonen.

Draper then one-timed a pass from Eaves, after Darren Helm battled for the puck in the corner, for his second goal in three games at 13:23.

“Our third and fourth lines were what I expected in Colorado (in Monday’s 4-3 overtime win) and didn’t get,’’ Babcock said. “I expect them to play with that kind of energy.’’

The Red Wings came back to tie the game at 3-3 in the second period, after Dallas had scored three goals in a span of 1:14— from Brad Richards, Mark Fistric and Jamie Benn -- to take a two-goal lead.

The Red Wings were reeling, but Lidstrom settled things down a bit by scoring at 8:56. He blasted in a one-timer on a pass from Valtteri Filppula, while Bertuzzi provided a screen.

“It was a tough minute and change, but we stuck with it,’’ Stuart said. “They got a little undisciplined at times, we capitalized. It was anybody’s game going into the third and we kept it simple, got the go-ahead goal and went from there.’’

The Red Wings led 1-0 after the first period, despite being outshot 12-4, on Hudler’s power-play goal at 1:36.

Bertuzzi, from the slot, corralled the puck after a shot by Lidstrom was blocked and made a nice, quick backhand pass to Hudler, who fired the puck into an open net before Lehtonen could get across to cover.

“I thought we played a real solid road game, especially when they scored three quick goals in the second,’’ Lidstrom said. “We didn’t give up, we worked our way into it again. We didn’t panic. We stuck to our game plan and slowly we took that game over.’’