ST. PAUL, Minn. -- The Phoenix Coyotes were worried that their reputation as a defensive team was in jeopardy.
On Wednesday night, they took a big step toward getting it back.
The victory snapped a three-game losing streak for the Coyotes. The Wild have lost two straight and scored a total of one goal in that stretch.
The Coyotes rank fourth in the league in goals per game, but they had allowed 20 goals in their previous five games before Wednesday.
They don't have a shutout this season and hadn't allowed fewer than two goals in a game since Oct. 29.
"We know we have to get back to playing a really tight defending game," Coyotes coach Dave Tippett said.
"Our offense has been very good, that hasn't been an issue. But we have to defend better and tonight hopefully was a step in that direction."
The Wild were playing their first game without leading scorer Zach Parise, who is expected to miss 2 to 3 weeks with a foot injury suffered on Monday in St. Louis.
Minnesota's offense was sluggish for much of the game, especially in the first period when the Wild were outshot 12-5 and fell behind 1-0.
The Wild struggled to adapt to new line combinations that were immediately juggled when center Mikael Granlund left the game and did not return after taking a hard hit on his first shift.
"It seems like every game right now we've got different guys going out with different guys. But there's no excuses," Wild coach Mike Yeo said. "That game was still there for us but we've got to make sure we're ready to start better, that's all."
Boedker kept the puck and fired a shot from the left faceoff circle that beat Wild goaltender Niklas Backstrom.
That was almost all the cushion Greiss needed. Playing in only his sixth game of the season, he said he appreciated having an early lead to take the momentum and ease some of the pressure on him.
"It was great," Greiss said. "We talked a little bit about getting the first goal and playing a solid defensive game. That's what we did."
Vrbata doubled the lead at 3:42 of the second period when he pounced on a pass from Tim Kennedy from behind the net and snapped the puck past Backstrom for his seventh of the season.
Dany Heatley brought the Wild within a goal midway through the third period when he buried a rebound that Greiss didn't handle cleanly.
Nino Niederreiter took a shot from the top of the slot that was tipped in front of Greiss. The puck bounced off his mask and fell to Heatley at the right post, where he got his fifth goal of the season.
But that was the closest Minnesota would get. Vrbata added an empty-net goal on a power play with 22.9 seconds left to provide the final margin.
"It's a start," Tippett said. "We played a solid road game. We came out and had a really good first period. We got up by one and had some chances to go farther than that.
"We took a few unfortunate penalties in the second and let them get a little bit of momentum, but then we weathered the storm in the third and got a solid two points."
Despite missing Parise, the Wild welcomed the return of two key players on Wednesday. D Keith Ballard had missed the past nine games with two broken ribs, while C Torrey Mitchell had missed three games with a lower-body injury. ... Phoenix is 6-0-2 in its past eight games in Minnesota.