Polak's assist came on David Backes' 10th goal of the season at 10:30 of the first period. Polak scored his first goal of the campaign at 2:51 of the third, following assists by Brad Boyes and Keith Tkachuk.
Minnesota's Nick Schultz and Pierre-Marc Bouchard both scored once. Niklas Backstrom was beaten three times on 23 shots for the Wild, whose record is 2-7-1 in December.
St. Louis went 0-for-3 on the power play, while the Wild finished 0-for-5.
Toddler uninjured after being knocked over by Obama family dog
Florida bear attack: Black bear mauls woman's face