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A scoreless overtime didn’t just pave the way for an appropriate addendum to Mikko Koivu’s 1,000th game, which was decided Sunday when the Wild captain buried the decisive goal in the shootout to finalize a 3-2 win over the Stars at Xcel Energy Center.

The five-minute stalemate was also the best the Wild has looked in an extra session this season.

And considering how maligned its play in that scenario has been — in the present and past — this progress emerged as one of the latest positives during the Wild’s recent run, one that has it on a season-high nine-game point streak (6-0-3) entering the opener of a three-game road trip Tuesday against the Florida Panthers.

“At this point,” winger Zach Parise said, “maybe getting through overtime is a win for us.”

Surviving to the shootout wasn’t happenstance.

After the Wild was burned just 32 seconds into the additional period Nov. 25 on the Rangers’ first shot, a 3-2 loss that dropped it to 0-4 this season in overtime and 12-32 all-time since the 3-on-3 format was implemented ahead of 2015-16, the team focused on the situation.

“We’re paying a little more attention to it because the guys were getting a little fed up with what was going on with it,” coach Bruce Boudreau said.

After the loss in New York, the Wild held a video session and practiced the setup after it returned from that road trip. The topic has also been discussed in its morning meetings.

“We’ve looked at clips,” goalie Alex Stalock. “We’ve really broken it down and said, ‘This is not an area where we play this style. This is not an area where we do this.’ And I think it worked.”

Plenty was different when the Wild matched up with Dallas.

For starters, the team won the initial faceoff — which happened only once in its previous overtimes. And by having the puck, the open ice becomes an asset that can be exploited. Without it, that much space makes the defensive players vulnerable.

“A big part of it was we won the opening draw,” Parise said of Sunday’s showing. “That makes a big difference. And I think we were smarter with the puck. How many times have we just lost that draw? I feel like we’ve never had the puck in overtime, so it makes it tough.”

Unlike its other overtime finishes, the Wild also didn’t get stung on the opposition’s first shot — a trend that contributed to the team’s slew of early exits and was a byproduct in some instances of it chasing the puck.

Besides losing the draw in the Rangers game, the same happened Nov. 2 against the Blues and Nov. 16 against the Hurricanes (both 4-3 finals). The Wild did get one shot off vs. Carolina before the Hurricanes capitalized on their first one at 1:33, but it had none before St. Louis connected on its initial puck on goal at 2:27. Boston’s first and only attempt Nov. 23, an end-to-end rush by Torey Krug, was also all the Bruins needed to end the action at 2:41 — this after the Wild won the opening faceoff, registered three shots and had another three either blocked or miss the net.

Against Dallas, Stalock stopped the lone puck directed his way.

“We controlled the play in overtime,” Stalock said.

What helped the Wild do that was the trios it rolled out.

Boudreau started winger Kevin Fiala, center Eric Staal and defenseman Jonas Brodin, the first time the team debuted two forwards after previously going with one forward and two defensemen.

Staal, Jason Zucker and Mats Zuccarello were the only veterans to log minutes up front, as Boudreau frequently utilized such younger forwards as Fiala, Jordan Greenway and Luke Kunin.

Fiala seemed particularly comfortable on the ice and was arguably the most dynamic player in overtime. He got off two shots on that first shift and accounted for the Wild’s third and final puck on net.

“We were pressuring,” he said. “We were aggressive. We had a few chances; myself I had like three chances that didn’t result. But just have to continue.”

In between rushes, the Wild also wasn’t afraid to utilize Stalock by passing off to him to reload. By doing so, it felt like the team had an edge.

“Puck control is so huge,” Stalock said.

These strides weren’t directly responsible for the victory Sunday, but they could have been. And if these habits continue, perhaps they will be the catalyst soon.

“I feel like it’s a good step,” Fiala said.