Evgeni Malkin beat Bryzgalov at the 8:21 mark of the third to draw the Penguins within a goal, but the visitors couldn't produce an equalizer.
Marc-Andre Fleury stopped 26 shots for Pittsburgh, which has dropped three of five.
Pittsburgh captain Sidney Crosby sat out the game against Philadelphia for precautionary reasons after a collision with teammate Chris Kunitz in Monday's loss to the Boston Bruins. Crosby also will miss Saturday's visit to the New York Islanders.
Philadelphia opened the scoring on a fluky goal as Briere's shot from the left point deflected off of two Pittsburgh skaters and past Fleury 6:38 into the contest.
Later in the first period, the Flyers were on the wrong end of a 5-on-3 power play. The fact that penalty killers Maxime Talbot and Kimmo Timonen were both without sticks only exacerbated the situation. However, Kunitz took a cross- checking penalty just as the first infraction ended to even things out at 4- on-4.
The Flyers increased their lead to 3-0 in the second period behind goals from Simmonds and Hartnell.
On a power play, the Flyers displayed tremendous puck movement. The red-hot Claude Giroux dished across the ice to Jakub Voracek in the right circle. Voracek then sent the puck through the crease to Simmonds -- uncovered at the back door -- and he swept it into an open net at 8:42.
A net-crashing Hartnell buried Andrej Meszaros' backhand feed at 13:32.
James Neal put the Penguins on the board 38 seconds later with a power-play goal, his eighth of the season.
The Flyers were 4-1-1 against the Penguins last season...Pittsburgh defenseman Brooks Orpik played in his 533rd career game on Thursday, tying him with Ron Francis for 10th place on the club's all-time list...Fleury has allowed three or more goals eight times in his last 10 starts.