Philadelphia was shut out in back-to-back games for the first time since February 2003 and the Flyers have not scored in 160:04 going back to Braydon Coburn's goal late in the first period of a 4-2 loss to the Buffalo Sabres on Nov. 27.
The Flyers have lost three straight and six of their past seven.
Mitchell scored at 13:38 of the second period when he picked up a loose puck in front of the Philadelphia net and scooped a backhand over the shoulder of Flyers goaltender Brian Boucher, who finished with 26 saves.