All five Philadelphia goals came in the final period, which began with the Blue Jackets owning a 3-0 lead.
The Flyers have won consecutive games while the Columbus meltdown led to its third straight loss.
Jakub Voracek and Braydon Coburn scored 62 seconds apart early in the third period to start the Philadelphia comeback, but Columbus moved two goals in front when Blake Comeau put a wrist shot past Steve Mason with 11:25 left in regulation.
Erik Gustafsson again brought the Flyers within one with 4:39 remaining and Giroux then became the hero with his two late goals.
Giroux tied the game with 3:36 left and his backhander with 1:48 to play gave the Flyers the lead.
The Wild's Curtis McElhinney stopped all 24 shots he saw during the first two periods and then gave up five goals on 15 shots during the third.
Mason made 24 saves to collect the unlikely win.