Savard's score 3:36 into the final period broke a 2-2 tie and triggered a late four-goal outburst.
Boone Jenner, Ryan Johansen and R.J. Umberger each followed with a goal for Columbus, which split a home-and-home series with the Flyers.
Nikita Nikitin and Corey Tropp had two assists apiece and Curtis McElhinney made 33 saves.
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