David Kampf and William Nylander scored, and Ilya Samsonov made 26 saves for the Maple Leafs (2-1-0), who have won two in a row.
"[Samsonov] looked really calm and settled in the net," Toronto coach Sheldon Keefe said. "You could tell he grew from one start to the next. That's what you are looking for is a guy to get comfortable. Not expecting to start, but it changes your day, your plans, and all those kind of things, but it didn't look like he missed a beat, so that was good to see."
Shane Pinto and Claude Giroux scored, and Anton Forsberg made 29 saves for the Senators (0-2-0).
"We defended really well and then we let them get to the net there with two minutes to go," Ottawa coach D.J. Smith said. "It's really disappointing, but if we play like that we're going to win lots of games.
"We've got to be a little more desperate [on the winning goal]. We've got to knock people down and we were fishing for the puck."
Samsonov said he found out at the morning skate that he would be starting after Matt Murray sustained an adductor muscle injury during the session.
"This is hockey, sometimes you have a bad situation with the team but I'm ready all the time," Samsonov said. "I got some hard practice the other day, and it doesn't matter what's going on, just get ready."
Nylander gave Toronto a 2-1 lead when took a cross-slot pass from Auston Matthews and shot over Forsberg's glove from the right hash marks on the power play at 13:24 of the third period.