Matthews took a pass from Morgan Rielly in the extra period and fired a shot that hit the stick of Edmonton's Leon Draisaitl before bouncing in off defenseman Darnell Nurse's skate and past goalie Mike Smith.
''I'm going to take that, for sure,'' Matthews said. ''It's frustrating when the puck's not going in, but as long as I'm getting chances I just try to stay positive and continue to push and shoot the puck and continue to think, `The next one's going in, the next one's going in.' Not really how I drew it up or ever envisioned it, but I'll take that.''
Matthews broke a tie with Oilers star Connor McDavid for the NHL goals lead with his 22nd. The Toronto star also had an assist.
Toronto overcame a two-goal deficit in the third period, with John Tavares cutting it to open with 7:39 left and William Nylander tying it with 3:22 remaining.
''Resiliency,'' Matthews said. ''We just stuck with it.''
Pierre Engvall also scored, and Jack Campbell made 17 saves to help North-leading Toronto win its third straight and improve to 22-10-2.
Leon Draisaitl had a goal and two assists for Edmonton, Tyson Barrie added a goal and an assist against his former team, and Nurse also scored. Mike Smith made 27 saves. McDavid had two assists to push his NHL-best points total to 62.
''It's a good team,'' Draisaitl said. ''We're a really good team. It's always tight games.''
The teams will complete the two-game set and the nine-game season series Monday night at Scotiabank Arena.
The Oilers played for the first time in a week after their three-game series in Montreal was postponed when two members of the Canadiens were added to the NHL's COVID-19 protocol list Monday.
''Our energy was all right,'' Oilers coach Dave Tippett said. ''Our execution was poor.''
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