Vladar made 29 saves for the Bruins (19-10-6), who went 3-2-2 on a seven-game homestand.
Boston led 2-1 entering the third period, but Jeremy Lauzon was called for holding at 5:21, and Sean Couturier scored on the ensuing power play with a shot from the top of the left face-off circle through a screen by James van Riemsdyk to tie it 2-2 at 6:56.
"That hurt us obviously," Bruins coach Bruce Cassidy said. "It was the only chance we gave up in the third period. Found the back of the net, good shot, through a screen. Unfortunately, overtime, we had couple of pucks on our stick that we weren't able to get to the net or get past the goalie, and they did."
Travis Konecny gave the Flyers a 1-0 lead at 10:15 of the first period. It was his first goal in 13 games.
"It was nice to get that one," Konecny said. "Honestly, I've just been trying to play the right way and play hard. And you know, it's so cliche, but if you just keep working and doing things, working hard for your linemates … it's a matter of time before a bounce will go your way."