"The lungs were going pretty hard tonight, but I think we played a pretty good road game," Sutter said. "To get that late goal by Thomas Vanek] to tie the game is huge, and obviously anything can happen in overtime, so we were lucky to get it, but we played really well."
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Loui Eriksson and Vanek scored, and Jacob Markstrom made 21 saves for Vancouver (18-21-6), which won for the fourth time in 17 games (4-11-2).
Jason Zucker and Daniel Winnik scored for the Wild (24-17-5), who have a point in seven straight home games (5-0-2). Devan Dubnyk made 22 saves and allowed more than two goals for the first time since giving up six in a 7-2 loss at the Colorado Avalanche on Jan. 6.
"That would have been a big win for us obviously," Zucker said. "It was kind of an up-and-down game. We carried the pace, and then they'd kind of take it. Back and forth a bit."
Vanek tipped in a Sam Gagner shot with 3:12 remaining in the third period to tie the game at 2-2.
"My kids are here, so it was great," Vanek, who went to the University of Minnesota from 2002-03 and played with the Wild from 2015-16 said. "It was a big goal this late in the game for our team. I just felt great that we tied it up. I thought for the most part both teams played a good game, and there wasn't too many chances against. It was a big goal for us and obviously to get that extra point in overtime was huge for us right now."