It was the first shutout of the season for Quick, matching his total for the lockout-shortened 2012-13 campaign. He had 10 the season before that and this was the 26th of his seven-year career.
Mike Richards scored with 36 seconds to go in the first period and Anze Kopitar delivered a goal with 7:42 left in the second.
Buffalo was unable to build on what was only its third win of the season on Tuesday against San Jose. The Sabres have the fewest number of points in the league with seven.