Bouchard, Martin Skoula and Stephane Veilleux 7 (empty net) scored one goal apiece.
Minnesota left wing Andrew Brunette sat out Saturday night's game because of a lower-body injury, ending the NHL's longest active consecutive-games streak at 509. He last missed a game Dec. 31, 2001 (shoulder).
Niklas Backstrom made 35 saves on 37 shots for the Wild, who snapped a three-game losing streak.
Nolan rose to 37 points in 48 career games against the Red Wings.
Detroit got goals from Tomas Kopecky in the second and Ville Leino in the third. James Howard was beaten four times on 28 shots for the Red Wings, who dropped to 8-2-1 in February.