Matthews, who scored twice, joined Dit Clapper (Boston Bruins, 1927-30), Dave Andreychuk (Buffalo Sabres, 1982-85) and Sergei Fedorov (Detroit Red Wings, 1990-93).
"I really try to score every game, so I don't know what to say (about the record)," Matthews said. "William Nylander] made an unbelievable pass on the first goal, and then [Mitchell Marner] with eyes in the back of his head on the power play, it was an amazing pass and I just tried to get it off as quick as possible."
[WATCH: [All Senators vs. Maple Leafs highlights]
Ilya Mikheyev had a goal and an assist in his NHL debut, Frederik Gauthier and Trevor Moore scored, and Frederik Andersen made 23 saves for the Maple Leafs, who had lost the previous five times they opened the season against the Senators. Tyson Barrie had two assists in his Toronto debut.
"It was a perfect start for them. We were nervous and they banged it in our net," Maple Leafs coach Mike Babcock said of the Senators taking a 1-0 lead 25 seconds into the first period. "Then we got three power plays in a row, we were borderline dysfunctional, we couldn't move. I thought once we got through that and were down 1-0, we came out and just played."