Ryan Carter, Charlie Coyle and Jared Spurgeon also had goals for Minnesota, which dealt its playoff nemesis Chicago its second straight loss.
Mikko Koivu added three assists, and Devan Dubnyk made 25 saves, as the Wild won their fifth straight at home to start the season.
Jonathan Toews scored twice for the Blackhawks, who finally snapped a 5-on-5 scoring drought. Brent Seabrook and Artem Anisimov had a goal each for Chicago and Scott Darling stopped 25 shots.
The Blackhawks have beaten Minnesota in the second round of the playoffs the past two seasons.
But the Wild have actually had the upper hand lately during the regular season, going 9-6-1 against Chicago in the last 16 games.
Two nights after setting a team record with a goal just 10 seconds into the game, Zucker started the scoring when he spun around with a loose puck and fired a quick shot past Darling.
Toews answered four minutes later and Seabrook gave the Blackhawks the lead. The Wild countered with goals from Carter and then Coyle, who scored with 11 seconds left in the first.
While Minnesota tries to prove itself against Chicago, this year's version isn't the same Blackhawks, either.
The defending Stanley Cup champions traded forwards Patrick Sharp and Brandon Saad and defenseman Johnny Oduya left as a free agent. The Blackhawks have also lost defenseman Duncan Keith to a knee injury.
It has led to the Blackhawks being the league's fifth-lowest scoring team entering Friday, averaging two goals per game. Chicago had won four of its past five but hadn't scored with the teams at full strength since Oct. 22 at Florida. That ended when Toews netted his second goal midway through the second period.
NOTES: Chicago F Marian Hossa didn't play in the third period because of a lower-body injury, the team announced. ... Wild F Justin Fontaine left the game in the second period and did not return after a knee-on-knee collision with Chicago F Andrew Desjardins. Minnesota announced Fontaine suffered a lower-body injury. ... Blackhawks D Erik Gustafsson made his NHL debut. ... Linesman Brian Mach, a Minnesota native, was honored before the game for officiating in his 1,000th NHL game.