The Flyers scored three times in the second period, with forwards Zac Rinaldo, Wayne Simmonds and Mike Testwuide beating Leafs goalie James Reimer in an 11-minute span.
Sean Couturier scored in the third period, and Flyers defenseman Matt Carle had a pair of assists in front of announced crowd of 18,480.
"We're just trying to prove ourselves. ... We all have opportunities here and we want to take advantage," said Couturier, who was drafted eighth overall last June and was playing in his first NHL-caliber contest.
"I was kind of nervous, but once you get going, you feel pretty good. I tried to approach it like it was any other game, but for sure it was something special."
The preseason matchup featured two pairs of brothers going to head to head, with established NHLers Luke Schenn and Phil Kessel suiting up for Toronto against Philadelphia prospects Brayden Schenn and Blake Kessel.
Toronto's Schenn, entering his fourth NHL season at the age of 22, was impressed with his younger brother's performance.
"I thought he played pretty well, nothing flashy but he was sound defensively, good on faceoffs and strong on the penalty kill," Luke Schenn said.
"There was probably some nerves, it being his first game with the Flyers and playing in front of a big crowd here at Air Canada Centre."
Brayden Schenn was a key part of the offseason trade that sent Mike Richards to the Los Angeles Kings, and Blake Kessel signed a free-agent deal last week.
Bobrovsky's biggest stop came during a Leafs two-man advantage when the game was already out of reach in the third period, going post-to-post to frustrate Clarke MacArthur.
Rinaldo opened the scoring at 7:25 of the second. He took a pass from Jakub Voracek at the blue line, beat a diving Schenn and swooped in on Reimer before sliding the puck between the goalie's legs.
Couturier made it 4-0 early in the third. The Leafs turned the puck over in the offensive zone, and the 2011 first-round pick wristed a shot past Reimer's glove at 2:40.
The Flyers went 1 for 5 on the power play, and Toronto was 0 for 9. The Leafs had a two-man advantage for a full two minutes midway through the third period, but Bobrovsky was able to preserve the shutout.