Marner won it with a one-timer on the power play after receiving a pass in the high slot from William Nylander.
"I don't think anyone really thinks I'm going to shoot that," Marner said. "The first passes I got, I looked at the net and saw a little bit of a lane and then the third pass I got I decided to try to get it to the net with John Tavares in front. Luckily it went in."
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Jason Spezza also scored, and Michael Hutchinson made 24 saves for the Maple Leafs (28-17-7), who have won three in a row.
"I thought we stayed with it," Toronto coach Sheldon Keefe said. "We knew it was going to be a hard game and it was, they played extremely hard and credit to them for the plan they put in place. On back-to-back games for them, it was clear how important this game was to them, but it was important to us as well."
Mark Borowiecki scored, and Craig Anderson made 34 saves for the Senators (18-24-10), who were coming off a 5-3 loss to the Washington Capitals on Friday.
Borowiecki gave Ottawa a 1-0 lead at 6:08 of the second period when his slap shot from the left boards beat Hutchinson blocker side through a screen.
"It was an interesting game, a little bit different style than what we're typically used to," Borowiecki said. "They play an interesting way, really try to hog the puck out there and hang on to it so you get some different looks, but I thought we adapted pretty well and played them tight."