Thomas had allowed markers to Matt Read and Claude Giroux in the first two rounds of the tiebreaker. But after David Krejci, Tyler Seguin and Patrice Bergeron all tallied for Bruins, the Boston goaltender needed only to make a final save to register the win.
Briere came down the middle, pulled up and unleashed a shot the Thomas partially blocked with his arm, allowing Boston to snap a four-game skid.
Thomas finished with 27 saves while Seguin and Chris Kelly scored in first period for Boston, which avoided its longest slide since 2010.
Read scored in regulation and Jakub Voracek tied it up with 4:17 left in the third period for the Flyers.
Philadelphia's Ilya Bryzgalov turned aside 31-of-33 shots.