The Wild had not won since Dec. 10 at Phoenix.
Minnesota started poorly again, giving up a goal to Taylor Hall just 1:24 into the game. The Wild then came up with unanswered goals from Mikko Koivu in the first period and from Jarod Palmer and Pierre-Marc Bouchard in the second.
Ladislav Smid brought the Oilers within one before Heatley's wrist shot gave Minnesota a 4-2 lead with 4:34 to go in the middle period.
Nikolai Khabibulin gave up four goals on 19 shots before being removed in the third period for Devan Dubnyk. Edmonton has lost eight out of 10.