"We spent a lot of the night chasing the game," Red Wings coach Mike Babcock said. "We knew what kind of game it was going to be before we started. We knew they were going to play tight."
Minnesota led 1-0 after the first period despite being outshot 17-5.
"We knew we were going to come out a little sluggish," Wild defenseman Ryan Suter said. "Backy kept us in it and we came out in the second period and played the way we should've."
Setoguchi opened the scoring 2:04 into the game when he swept in a shot from the bottom of the right circle for his 10th goal. Setoguchi's second goal of the game came on the power play with 2:45 left in the second period, putting in a rebound to give Minnesota a 4-1 lead.
Brodziak's power-play goal 3:51 into the second period made it 2-0 when he put in a one-timer shot from the edge of the crease, his fifth goal, off a pass from Jared Spurgeon.
Nyquist put Detroit on the scoreboard 9:09 into the middle period with his first goal. He capitalized on Spurgeon's turnover at the Red Wings' blue line for his first goal of the season, on a breakaway.
"It was a broken play at the blue line, I don't know what happened," Nyquist said. "I got it behind the D man and I came skating in all alone. I tried to make a move and fortunately, it went in."
Koivu restored the Wild's two-goal lead with 9:11 left in the second on spin-around shot from the high slot, which went in off Jimmy Howard's glove for Koivu's seventh goal.
Setoguchi got his second goal of the night, with 2:45 left in the second by putting in Dany Heatley's rebound.
"That's what you need. We've just got everybody contributing right now," Yeo said. "Getting it from the power play, getting it from different lines."
Miller got his third goal of the season, on the power play, in the final minute to cap the scoring.
An apparent goal by Detroit's Jordin Tootoo 7:30 into the first period was waved off because of a high stick call. But replays showed the puck went off the glove of Heatley instead of the stick of Miller.
Detroit RW Patrick Eaves missed the game with a sore cheekbone. The Red Wings recalled Nyquist, a center, from their AHL affiliate in Grand Rapids on Wednesday. ... Minnesota C Mike Rupp and D Tom Gilbert both missed their second games with lower-body injuries.
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DETROIT, MI - MARCH 20: Zach Parise #11 of the Minnesota Wild shoots the puck in warm-ups before an NHL game...