Owen Tippett scored the tying goal early in the third period for the Flyers (2-2-1). Dan Vladar made 15 saves.
"We knew we were in the game all along," Tippett said. "Low-event game, low-shot game. Just waiting for one to break through. I think we did a good job with staying up on the bench and waiting for opportunities."
Vladimir Tarasenko scored for the Wild (2-3-1), who have lost three in a row, including 5-1 at the Washington Capitals on Friday. Jesper Wallstedt made 19 saves.
"Trying to play our best game every night," Tarasenko said. "It's not like we come and don't want to play ... we have to work on staying on the same program for all 60 minutes."
Tarasenko gave Minnesota a 1-0 lead at 1:55 of the second period. The forward made a play to hold a bouncing puck in at the blue line and then dumped it into the slot. Marco Rossi corralled the loose puck, and as he was skating backwards toward the corner on the left side, passed it back to Tarasenko who found open ice in the circle and beat Vladar with a one-timer.
The goal was upheld after the Flyers challenged for offside.
"It's nice to score goals, but it's nicer to do it when the team gets a good result in the end," Tarasenko said.