Rittich made 28 saves for the Flames (7-5-1), who were coming off a 3-1 win at the Toronto Maple Leafs on Monday.
"I thought we just sat back a little too much maybe," said Sabres captain Jack Eichel, who scored in the first period. "Obviously, they had a good push, but I just didn't think we played good enough. I thought there wasn't enough compete and enough fire. We were sloppy. I thought at times we were OK in the [offensive] zone, but I thought we relied on our goalie too much."
Hutton made 36 saves for the Sabres (6-4-2), who have earned at least a point in five straight games (3-0-2) but lost two in row.
"He's really given us some really good, solid goaltending and been asked to stand on his head," Buffalo coach Phil Housley said. "It's unfortunate, because even though we didn't play up to our capability and it was sloppy and we looked slow at times, we were disconnected, we didn't play as a team, he still gave us an opportunity."