Enroth made 29 saves two days after he stopped all 15 shots he saw in relief of Ryan Miller against Philadelphia.
The Sabres snapped a two-game skid and left the Flames with a 1-1 record on their three-game road trip.
Alex Tanguay tipped in a shot exactly four minutes later for Calgary's only goal.
Henrik Karlsson stopped 42-of-44 shots in a losing effort.
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Aaron Carter is still in love with Hilary Duff