"I thought it was a really good effort by us," Matthews said. "A lot of really good things that we did tonight, but it's going to be a long series. That's a really good team on the other end."
Jack Campbell made 24 saves, Mitchell Marner had a goal and two assists, and Morgan Rielly and Ondrej Kase each had two assists for the Maple Leafs, who are the No. 2 seed in the Atlantic Division.
Toronto went 5-for-5 on the penalty kill.
"Our team seemed to be unflappable tonight," Toronto coach Sheldon Keefe said. "The kills that we have early, we get an early kill, no problem. The five-minute major, no problem. We just go out, go to the face-off, get our work done. In fact, it turned into a positive, the chances we were able to generate, the life we were able to generate.
"All the way through, our team was extremely focused and went out and executed, so it was a good night for us, but it was one night. Put our head on the pillow tonight and enjoy it and wake up tomorrow and then it's done, it's over. The Tampa Bay Lightning will be a far better team when they come back in here."