Calgary's Joni Ortio, in his eighth NHL start, outdueled Buffalo's Nathan Lieuwen, who made his first.
Ortio gave up one goal on four shots in the first period -- Drew Stafford's wraparound after a Calgary turnover behind the net -- and finished with 13 saves.
Joe Colborne scored the other goal for the Flames, who got their third win in four games.
The Sabres dropped their seventh in a row, all in regulation. It matched their seven-game losing streak to start the season.
Lieuwen was recalled from Buffalo's AHL affiliate in Rochester on Sunday and made his NHL debut later that day in a 2-0 loss to Montreal after Jhonas Enroth left 36 minutes in with a lower-body injury.
The 22-year-old, playing for the fourth time in five days after starting games for Rochester on Friday and Saturday, made 23 saves.
Swim Week Miami Beach 2014 [PHOTOS]