The Wild twice overcame a one-goal deficit and shook off a 6-2 drubbing at the hands of Montreal 24 hours earlier. It was the Wild's fifth win in six games.
Jason Pominville lifted Minnesota into a 1-1 tie in the first period and Jonas Brodin deadlocked the contest at 2-2 in the second.
Koivu then came through with the game-winner on a wrist shot, his fifth goal of the season.
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