Sanheim made it 2-0 56 seconds into the second period when he took a cross-ice pass from Garnet Hathaway and beat Samsonov with a wrist shot from the right circle.
Frost pushed it to 3-0 at 16:26 with a wrist shot from the high slot.
When the teams played here March 14, the Maple Leafs led the Flyers 3-1 after two periods en route to a 6-2 victory.
"We knew they were going to be better and have a lot of urgency and come out with some pace," Tavares said. "We just maybe weren't as sharp as we were defensively."
William Nylander cut it to 3-1 at 1:11 of the third period with a power-play goal, scoring on a snap shot from the left circle.
Bertuzzi made it 3-2 at 10:16, putting in a backhand pass from Morgan Rielly behind the net.
Laughton extended the lead to 4-2 at 13:00 on the rush after coming out of the penalty box, scoring in front off a wraparound pass from Tippett.
"When they score their first goal in the third period on the power play, you know it's going to be one of those games in the third period that's going to be close," Flyers coach John Tortorella said. "To have some of our kids play in that situation and play with some poise, go through that experience, it's huge to come out with a result.
"It doesn't matter how we get the results, through the front door, back door, side door, however we do it, we need to get a result."