Hartnell also had a goal, and Ilya Bryzgalov stopped 25 of 27 shots -- including 13 of 14 in the third period -- as Flyers (17-7-3) moved past the Penguins into first place in the Eastern Conference by winning their fourth in a row.
Briere gave the Flyers an early lead with one of the more curious goals of the season. He took a pass from Simmonds in the left circle, spun and fired a shot. The puck hit Pens defenseman Robert Bortuzzo in the circle and then went off his blue-line partner, Brooks Orpik, and behind Fleury at 6:38 of the first period.
Philadelphia made it 2-0 midway through the second with a power-play goal. Giroux made a great pass across the Pittsburgh zone to Jakub Voracek, who was at the edge of the right circle. When Fleury came out to deny his shot, Voracek sent a pass to Simmonds in front, and Simmonds stuffed it into the net at 8:42 for his sixth of the season.
"I think he's in his best spot in front of the net," Flyers coach Peter Laviolette said. "He gets in there, and he's not afraid to wrestle big guys and take some abuse and he does a good job of controlling his temper because it can get hot in that area. That's a hard area to get to and he does a good job of maintaining his focus and able to get his stick down and make plays. But I thought he had a strong game tonight."
After going seven games without a goal, Simmonds has two in his last three games. It also was his first multi-point game of the season.
"It's always good to contribute offensively when you can," said Simmonds. "I thought I'd be getting opportunities, I just haven't been burying my chances. Tonight I had 2 points and that's a good start."
Simmonds is one of the many additions to the Flyers this season, and Briere said the learning process is an ongoing issue.
"It takes time," Briere told NHL.com. "It doesn't happen overnight. Every game we're still learning about each other, little plays. We try to talk a lot, too. Try to find out where we're going to be and like to hang out on the ice. Tonight was a good game, hopefully a step in the right direction. Have to keep going."
Hartnell made it 3-0 when he drove to the net and rammed home an Andrej Meszaros centering pass. The goal was his 13th of the season and gave him a goal in a career-best fourth straight game.
"I've got to be on my game to play with (Giroux), to play with Jaromir Jagr," said Hartnell. "I work hard every day in practice, don't take it for granted. And I just go to the net, that's where I get my goals."
Neal's power-play goal at 14:10 of the second got the Penguins on the board. Malkin beat Giroux on a faceoff, then after Matt Niskanen returned him the puck in the left circle, Malkin found Neal alone in the right circle. Neal had time to corral the pass and shoot it under the crossbar above Bryzgalov's glove.
That made it 3-1, but it was a first-period 5-on-3 power-play opportunity earlier that the Penguins were lamenting. Trailing 1-0, it was a tremendous opportunity to knot the game. At one point two of the three Philadelphia penalty killers lost their sticks, but they could manage just one shot and as the first Philadelphia player left the penalty box, Chris Kunitz was whistled for a penalty, ending the Pittsburgh advantage.
"It was an opportunity for us, 5-on-3 and two guys lost their sticks," Penguins coach Dan Bylsma said. "It was certainly a missed opportunity when you get that 5-on-3 and have it for a minute and don't convert. You feel like you let one slip and didn't capitalize."
The Pens pushed hard in the third period, taking advantage of a Philadelphia team that battled from a 3-1 deficit for a 4-3 overtime victory the night before in Buffalo. They outshot the Flyers 14-7 but only had Malkin's 10th goal of the season to show for it.
"I think they came on a bit at the end," Simmonds said. "We weren't getting pucks deep, weren't doing things Laviolette told us to do and it came back to bite us a little bit."
However, they had Bryzgalov to bail them out.
"I thought he was really steady, especially at the end," Laviolette said. "He shined in the last 10 minutes of the game, last 12 minutes of the game when it seemed like they were starting to press a little bit and the puck was coming at our net more. I thought he did a good job of staying focused and making the saves we needed him to for us to walk out with the two points."
Contact Adam Kimelman at firstname.lastname@example.org. Follow him on Twitter: @NHLAdamK
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