The Flyers have opened the season with three straight victories and are one of seven teams in the NHL without a loss.
Claude Giroux, Chris Pronger and James van Riemsdyk all scored in the opening period to give the Flyers a 3-1 lead, but the defending Western Conference champion Canucks eventually rallied to tie it 3:39 into the third on a power-play goal from Daniel Sedin.
Meszaros put Philadelphia back in front 61 seconds later, producing his first goal of the season on a wrist shot that got past Roberto Luongo.
The goal for Giroux was his third of the campaign, making him the fifth player in the league to reach that total in the young season.
Luongo gave up all five goals on 26 shots.
Ilya Bryzgalov made 36 saves for the Flyers. He has been in goal for all three of the Philadelphia wins.