Alex Galchenyuk scored his first goal with the Wild to tie it 3-3 with 4:45 left in the third period and scored the deciding goal with a deke in the fifth round of the shootout.
WATCH: [All Wild vs. Canucks highlights]
Evason, who took over for the fired Bruce Boudreau on Friday but lost his debut Saturday, 2-0 to the San Jose Sharks, couldn't bring himself to watch Galchenyuk's attempt. He knew he had his first NHL win as a coach when he saw the reaction of his three children, who were in the stands.
Evason's son is with the Wild for their dads trip, and his two daughters joined him for this game.
"I didn't watch, I watched, didn't watch the shootout, and then the last one, I knew where the kids were with all the dads and mentors and I just looked up at my three kids and watched their reaction and all three of them jumped up in the air so I knew we scored," Evason said. "Pretty cool. It's amazing. You hear things happen for a reason and to have my three children here was awesome."
Devan Dubnyk made 31 saves in his first start in four games for the Wild (28-24-7), who trail the Calgary Flames and the Arizona Coyotes by five points for the first wild card into the Stanley Cup Playoffs from the Western Conference.
"These are the kind of games you can really build off," Dubnyk said. "Obviously, being up a goal going into the third, we'd like to finish it that way, but it doesn't matter one way or the other. When you battle to tie it up and then win it like that it can be a boost for us. It was definitely a good feeling."