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.
Members of Congress to keep receiving porn magazine
Rosie O'Donnell unveils nearly 50-pound weight loss