Jonathan Toews scored twice to help the 2.
Dave Bolland, Andrew Shaw and Jimmy Hayes each had a goal and an assist while Marian Hossa also scored for the Blackhawks, who have won four of five. Corey Crawford allowed two goals on 27 shots.
Jason Pominville had both goals for the road-weary Sabres, who have dropped 10 straight games as the visitors. Jhonas Enroth gave up six goals on 35 shots in defeat.