The two teams had combined to score four goals in the game's first 8 minutes when Brodie, a rookie defenseman, broke a 2-2 tie with a shot that trickled through the legs of Wild goalie Niklas Backstrom 8:45 into the contest.
Mark Giordano and Lee Stempniak also scored for Calgary, which salvaged one win on a four-game road trip.
Miikka Kirpusoff recovered from his poor start, earning the victory with 19 saves.
Backstrom allowed three goals on eight shots before exiting. Harding ended with 25 saves.
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