Minnesota won its fourth in a row and has captured six out of seven to take the lead in the Northwest Division.
Setoguchi produced the only first-period goal 2:04 into the contest and he gave the Wild a 4-1 lead with 2:45 to go in the second on the power play. He has 11 goals for the season.
Niklas Backstrom made 36 saves to slow down the busy Detroit offense and hand the Red Wings their fourth loss in six outings.
The Detroit goals came from Gustav Nyquist and Drew Miller, whose power-play score was recorded with just 14 seconds left in the third period.
All four Minnesota goals came against Jimmy Howard on a mere 19 shots.