Chychrun beat Ukko-Pekka Luukkonen with a snap shot from the right circle off a backhand pass from Aliaksei Protas, who was behind the net.
Ryan Leonard scored, and Charlie Lindgren had 29 saves for the Capitals (33-27-7), who had lost four of their past five games (1-4-0).
Sam Carrick scored, and Luukkonen made 19 saves for the Sabres (40-20-6).
Carrick gave Buffalo a 1-0 lead at 6:02 of the first period. Beck Malenstyn looped around the back of the net to the left circle and sent a no-look backhand pass to Carrick on the back door for the tap-in by Lindgren’s left skate.
Leonard scored for a third straight game to tie it 1-1 at 2:14 of the second period. He intercepted a pass intended for Logan Stanley at the left point and skated to the right circle for a snap shot that beat Luukkonen inside the far post.
