John Tavares and Calle Jarnkrok also scored and Morgan Rielly added two assists to help the Maple Leafs rebound from an opening 4-3 loss at Montreal on Wednesday night.
''Good bounce-back win.'' Matthews said.
Nic Dowd and Marcus Johansson scored for Washington, coming off a 5-2 home loss to Boston on Wednesday night. Charlie Lindgren stopped 36 shots.
''A start we don't want to have,'' Washington captain Alex Ovehckin said. ''A wake-up call.''
Matthews scored at 6:55 of the third, his first goal of the season after leading the NHL last season with 60. Mark Giordano found a seam on a point shot that Matthews got a piece of with his stick before it handcuffed Lindgren and dribbled over the goal line.
''We had a frank discussion this morning,'' Toronto coach Sheldon Keefe said. ''The guys responded really well.''
Samonov and the Maple Leafs held on late, killing two penalties and weathering a stretch with Lindgren off for an extra attacker.
''A lot of emotion in the first period,'' the Russian netminder said. ''First game with the Leafs for me and (against) my old team.''
Toronto opened the scoring at 6:40 of the first period on a power play that finally clicked when Rielly found Tavares at the lip of the crease with a slick feed.
''We talked about being more patient with our game,'' Tavares said. ''We tried to do a little too much (in Montreal), caught us chasing a little bit.''
The Capitals responded at 9:57, with Dowd scoring from close range. Johansson gave Washington the lead on a shot off the rush with 6:08 left in the period.
Toronto tied it at 4:03 of the second. Alexander Kerfoot took a pass from Rielly at the offensive blue line and delayed before finding Jarnkrok with a terrific feed for his first with the Maple Leafs after signing in free agency.
Samsonov was drafted 22nd overall by Washington at the 2015 draft, but didn't receive a qualifying offer from Washington, making him a free agent. The 25-year-old was 52-22-8 with a .902 save percentage and 2.81 goals-against average in 89 regular-season appearances with the Capitals.
Capitals: Host Montreal on Saturday night to open a two-game homestand.
Maple Leafs: Host Ottawa on Saturday night to continue a four-game homestand.
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