Philadelphia won for the sixth time in eight games, besting Niklas Backstrom a season-high six times on 28 shots.
Danny Briere, Andreas Nodl and Ville Leino all had a goal and an assist for the Flyers.
The only goal against Bobrovsky came from Patrick O'Sullivan early in the third period, briefly trimming the Wild's deficit to 2-1.
Philadelphia scored three times in the third to put the game away.
The Flyers recorded their most one-sided win over Minnesota since the Wild entered the NHL in 2000.
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