Ottawa scored its third goal in 4:35 when Chris Tierney slapped a loose puck in the slot to make it 4-2 at 15:03.
"We just had a really poor response after we took the lead," said Tavares, the Toronto captain. "We controlled a lot of the game, obviously playing in their half of the ice, got a big goal. Just a very poor response, gave them life, and we weren't able to establish our game again."
Stepan tapped the puck into an open net for a 5-2 lead at 6:15 of the third.
"I thought we did a good job of working as five-man units," Stepan said. "What I liked is that, in the third, we didn't just sit back. We pushed the pace a little bit and played some offense."
Tavares scored on the power play with a wrist shot from the left face-off dot to cut it to 5-3 at 7:07.
The teams play here again Saturday 7 p.m. ET; ESPN+, CBC, SNO, TVAS2, NHL.TV).
"That's a great team over there, very skilled," Tkachuk said of the Maple Leafs. "I think we're all very excited for tomorrow."
NOTES: Maple Leafs defenseman Morgan Rielly was minus-4 in 23:22 of ice time. ... Defensemen Erik Gudbranson (five blocked shots), Braydon Coburn (assist), and Josh Brown (four hits), and forwards Evgenii Dadonov and Cedric Paquette (three hits) each made his Senators debut. … Chabot's goal was the 30th of his NHL career, moving him within one of Steve Duchesne for sixth in Ottawa history by a defenseman. … Batherson, Zaitsev and Josh Norris each had two assists for the Senators.