Tuch received a pass from Dylan Strome and beat Ukko-Pekka Luukkonen with a wrist shot from the slot in his first game against his former team.
Tuch, who is from nearby Syracuse, New York, played the past five seasons with Buffalo before being acquired by Washington on June 26 in a sign-and-trade deal that netted him an eight-year, $84 million contract.
Strome had two goals and an assist for the Capitals (6-4-0), who have won three of their past four. Jordan Kyrou and Jakob Chychrun each had two assists, and Charlie Lindgren made 18 saves.
Jack Quinn, Josh Doan and Noah Ostlund scored for the Sabres (4-4-3), who have lost three in a row and four of five (1-1-3). Luukkonen made 30 saves.
Quinn gave Buffalo a 1-0 lead at 6:27 of the first period when he received a pass at the left wall from Olen Zellweger, skated to the net and lifted a shot past Lindgren.
Doan extended it to 2-0 at 10:36. Ryan McLeod intercepted defenseman Chychrun’s pass behind the goal and passed to Doan, who scored on a one-timer from the right face-off dot.
Tuch cut it to 2-1 at 16:10 after Sabres forward Tage Thompson tried to block his centering pass and the puck deflected past Luukkonen.
Strome tied it 2-2 at 2:59 of the second period, controlling a bouncing puck in front of the net and sliding a backhand shot inside the right post.
Forty-six seconds after Lindgren made a left pad save to stop Zach Benson on a breakaway, Strome gave Washington a 3-2 lead at 17:24 when he skated across the low slot, received a pass from Kyrou behind the goal line and snapped it in.
Ostlund tied it 3-3 at 2:20 of the third period when his shot deflected in off Capitals defenseman Matt Roy.
