It was Minnesota's first regulation win since Jan. 29 and just the second time it scored at least three goals in regulation over the last nine games.
Damien Brunner and Pavel Datsyuk scored for Detroit, which has lost three straight for the first time since March 10-21 of last season.
After Heatley snapped a nine-game scoring drought to make it 2-1, Zucker went coast-to-coast and scored his first NHL goal to tie it.
Zucker was called up on Saturday to try and spark the Wild's offense. The 2010 second-round pick showed off his speed and made a slick move on Valtteri Flippula to break free and score unassisted.
Mitchell scored his first goal in a Wild uniform off a faceoff scrum to give Minnesota the lead 30 seconds later.
Despite allowing 14 shots and hearing boos from the home crowd, the Wild only trailed 1-0 after the first period.
Brunner whacked the puck past rookie goalie Darcy Kuemper to give Detroit the lead at 8:48. Ryan Suter couldn't clear the bouncing puck and Brunner took advantage.
Kuemper was making his second NHL start after stopping 28 of 30 shots in his debut Tuesday, a 2-1 loss at Vancouver. He made 29 saves on Sunday.
Regular Wild goalie Niklas Backstrom had the flu and was backing up Kuemper.
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Datsyuk, back after missing a game with a shoulder injury, beat the rookie with a wrist shot from outside the left circle 20 seconds into the second.
Then the Wild woke up and scored three times on rookie goalie Petr Mrazek in a span of 4:10 to take a 3-2 lead.
It wasn't just the Wild's offense that got rolling in the second period. Thanks to a diving save by Kuemper early and strong defense throughout, Minnesota killed a four-minute high-sticking penalty to close the second.
Besides the stretch in the second, Mrazek was solid, stopping 24 shots.
The Red Wings are now 8-2-2 in their last 12 games against Minnesota.
NOTES: Minnesota's Pierre-Marc Bouchard and Justin Falk missed the game due to illness. Zenon Konopka was a healthy scratch. ... Henrik Zetterberg had two assists and has 20 points in his last 14 games. ... Zucker led AHL Houston with 19 goals and 41 assists. ... Mikael Samuelsson returned from a groin injury and played in his third game of the season for Detroit.
Press; By ADAM CZECH]
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