The 30-year-old forward was acquired from the Buffalo Sabres in a sign-and-trade deal (eight years, $84 million; $10.5 million average annual value) on June 24.
Jakob Chychrun had a goal and an assist, and Ryan Leonard and Cole Hutson also scored for the Capitals in their season opener. Pierre-Luc Dubois and Dylan Strome each had two assists, and Logan Thompson made 31 saves.
Sebastian Aho and Logan Stankoven scored for the Hurricanes (0-1-1). Brandon Bussi made 22 saves.
Tuch gave Washington a 1-0 lead at 6:33 of the first period. Dubois stripped the puck from Bussi behind the Carolina net and fed a backhand pass to Tuch, who scored between the circles into the open net.
Hutson extended it to 2-0 at 11:33, scoring on a short-side snap shot off a pass from Ilya Protas.
Tuch’s second goal of the game pushed it to 3-0 at 14:23, tapping the puck into the net after Tom Wilson’s shot from above the left circle trickled through Bussi.
Chychrun made it 4-0 on the power play at 1:36 of the second period on a wrist shot from inside the blue line.
Aho’s power-play goal cut it to 4-1 at 16:50 off a feed from Andrei Svechnikov.
Leonard answered eight seconds later to extend it to 5-1 after he drove the net and redirected a pass from Strome.
Stankoven cut it to 5-2 at 10:50 of the third period when he tipped K'Andre Miller's wrist shot from inside the blue line.
