Jake Allen made 24 saves in the win, the Blues' second against Buffalo in the last week.
David Legwand scored for the Sabres, winless in their last five games.
Legwand took advantage of Nicolas Deslauriers' hard forecheck, snaring a loose puck from behind the net and sliding it off Allen's pad and across the goal line at 16:45 of the second period.
Buffalo missed two good chances to double its lead early in the third, including when Brian Gionta put an in-close shot off the crossbar.
