Spurgeon took a pass from Michael Keranen and beat Ondrej Pavelec high on the glove side for Minnesota's third power-play goal in four chances.
Mikael Granlund, Erik Haula and Nino Niederreiter also scored for Minnesota (1-1-1).
Nicolas Petan, Matt Halischuk and Grant Clitsome scored for Winnipeg (1-2-0).
Pavelec stopped 20 shots for the Jets, and Niklas Backstrom made 14 saves for Minnesota.
Petan and Granlund traded first-period goals before Haula scored on a penalty shot late in the period to give the Wild a 2-1 lead. Halischuk and Niederreiter exchanged second-period goals, and Clitsome scored 40 seconds into the third.