The Flyers moved within two points of Pittsburgh for fourth place in the Eastern Conference, which carries with it home-ice advantage in the opening round of the playoffs.
Toronto, which is out of playoff contention, has lost three in a row.
Schenn scored the game's first two goals in the opening 11 minutes and Simmonds tallied in both the second and third periods. Philadelphia had three power-play goals and came up with a shorthanded one as well, from Matt Read in the second period that gave the Flyers a 4-1 lead.
Toronto has lost 11 straight at home, a franchise record. Their last home victory came Feb. 6.
The lone goal for the Maple Leafs came from Mikhail Grabovski in the second period.
Sergei Bobrovsky had to make only 16 saves to collect the victory. Jussi Rynnas, in only his second NHL appearance, was left in to absorb all seven goals on 23 shots.