Fluery turned aside 27-of-28 shots, allowing just a Mikael Backlund goal with 8:31 remaining in the final period.
Backlund's goal snapped a 196-minute, 59-second home-ice scoring drought for the Flames, but wasn't enough to prevent their 11th loss in 13 games overall.
Reto Berra made 24 saves.
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