Auston Matthews scored for the second game in a row, and Ilya Samsonov made 23 saves for the Maple Leafs (5-4-2), who went 1-2-2 on a five-game road trip that ended Sunday with a 4-3 overtime loss to the Anaheim Ducks.
"It was a tough game, a little bit hard for me," Samsonov said. "I don't like it when [there's] not a lot of shots. It's really hard because all the time 3-on-2, 2-on-1 and confidence [is] a little bit lower, but the result is great. This is what we needed."
Joel Farabee and Owen Tippett scored, and Felix Sandstrom made 39 saves for the Flyers (5-3-2), who lost 1-0 in overtime against the New York Rangers on Tuesday.
"For the most part, I thought our guys had a lot of 'try,'" Philadelphia coach John Tortorella said. "Some guys, no. That's where some of my frustration is, not so much in the result, but how guys, the effort that is put in sometimes.
"It hasn't come together. It's still a ways away, and that's part of our job as a coaching staff, to bring it together. It's going to take some time. We've found a way to win some games with some really good goaltending that's given us an opportunity. But we still have a ton of work to do to be considered a team that's come together."
Tavares put Toronto up 2-1 at 18:37 of the first period when he one-timed a pass from William Nylander over Sandstrom's glove from just inside the blue line.
Samsonov made a sprawling left pad save on Tony DeAngelo's shot from the top of the goal crease on the power play seven seconds into the third period to keep Toronto up 2-1.
"This was a tough game for a goalie to play in," Maple Leafs coach Sheldon Keefe said. "Not only were there not a lot of shots, but there was not a lot of activity on our half of the ice. Sometimes in games when you're not getting shots, you're still in your own end having to track the puck and move, but he was kind of standing in the net waiting for the next save. So, for him to make a big save at a key time and so early in a period, that shows us he was sharp and ready. Those are the kind of things we talk about, owning each moment that comes your way."