The Wild began the night in 11th place in the Western Conference but were only four points behind fourth-place Chicago in the tight battle for playoff positions.
Minnesota fell behind 3:13 into the game on the third goal of the season by Sean Avery, but Theodore went on to make 35 saves in helping the Wild snap a two-game skid.
Kyle Brodziak tied it early in the second on the power play and Casey Wellman put the Wild in front with 7:24 to go in the middle period. Pierre-Marc Bouchard gave Minnesota some insurance midway through the third.
Henrik Lundqvist allowed the three Minnesota goals on just 19 shots. New York lost its third straight and is in danger of slipping out of a playoff position. The Rangers began the game in seventh place in the Eastern Conference, just one point ahead of Carolina and three in front of Buffalo.