With 61 points, Minnesota moved two ahead of Chicago for first place in the Western Conference. The Wild have four games in hand.
"To beat this team eight times in a row is really something," said Wild coach Bruce Boudreau, who lost to the Blackhawks in the 2015 Western Conference Final while coaching the Anaheim Ducks. "I don't understand how you can do it. I wish I'd had that knowledge a couple years ago, but it's a new year and it's just one in a row right now."
WATCH: All Wild vs. Blackhawks highlights
Patrick Kane scored two goals to give the Blackhawks a 2-0 lead early in the second period, but Minnesota tied the game 2-2 before the period ended on goals by Nino Niederreiter and Chris Stewart.
Pominville made it 3-2 at 5:08 of the third when he picked a rebound off the end boards and shot it past goaltender Corey Crawford.
"It's nice to get one and help the team out in a good situation," said Pominville, who hadn't scored since Nov. 29. "I've obviously felt a little snake-bitten lately. I knew it was going to come. I was getting too many looks to not put one in. It came at a pretty good time."
Dubnyk stopped all five Chicago shots on goal in the third, and Blackhawks defenseman Brent Seabrook hit the left post with 36 seconds left. Crawford made 29 saves. Chicago also lost 6-0 at the Washington Capitals on Friday and has lost its past two games after winning four straight.
"As a group, I think there's things we can learn from this game, or the game in Washington," Kane said. "But [they're] two good hockey teams. Both of them are playing really well at this time of year. [It's a] good way to kind of judge yourself, where we're at. Might be a little bit of a wakeup call to see how good we really are."