Marek Zidlicky, Greg Zanon and Martin Havlat also scored for the Wild, who have won four of their last five but have only two road wins this season.
Koivu scored what proved to be the game-winner at 17:29 of the third period to give Minnesota a 3-1 lead. His goal was followed 29 seconds later by Zanon's first goal of the season.
Niklas Backstrom made 37 saves in the win. Toronto's Jonas Gustavsson faced 30 shots.
Alexei Ponikarovsky and Phil Kessel scored for Toronto.
Ponikarovsky tied the score 1-1 in the first period but did not score again until Kessel's goal with under two minutes to play.
Copyright 2009 by United Press International.
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