Ilya Mikheyev pushed the lead to 4-1 at 1:39 of the second period.
Marner put Toronto ahead 5-1 at 3:45 when he got around Mike Reilly and shot over Murray's left shoulder from below the right circle.
Connor Brown scored to make it 5-2 at 7:37, and Nylander responded at 11:00 on the power play to make it 6-2.
"It had been a lot of games without a point (six), so obviously it gets to you a little bit, so it was nice to get a goal and assist today for that reason," Nylander said.
Toronto outshot Ottawa 14-9 in the second period.
"I thought we came out and had a much better first period than our last outing on Wednesday, but I think our second period was our best period by far," Matthews said. "I thought we really controlled the play and didn't give them too much space. We kept coming wave after wave, all four lines and three pairs of defense."
Drake Batherson banked a shot off Maple Leafs defenseman Mikko Lehtonen's skate at 11:11 of the third period to cut it to 6-3. John Tavares made it 7-3 at 16:53 with his first goal in seven games.
NOTES: Matthews did not play in a 4-2 win at the Edmonton Oilers on Jan. 22 and has 20 points (14 goals, six assists) in the 12 games since. ... Thornton is the oldest player (41 years, 231 days) in Maple Leafs history to score at least three points in a regular-season game. ... Toronto played without forward Zach Hyman, who is day to day after he was injured Wednesday. … Ottawa was without defenseman Thomas Chabot, who was a late scratch and is day to day with an undisclosed injury.