Jeff Carter and Mike Richards added a goal and two helpers each while Joffrey Lupul and Scott Hartnell also lit the lamp for the Flyers, who have won four in a row and five of six, and moved two points ahead of Pittsburgh into second place in the Atlantic Division.
"You don't expect to put this kind of run together," said Lupul when referring to the Flyers' steady rise after an 0-3-3 start to the season.
Martin Biron stopped 23-of-26 shots for his third win in four starts.
Jordan Staal, Eric Godard and Ruslan Fedotenko tallied for the Penguins, who have dropped four of five.
Dany Sabourin allowed all six goals on 27 shots in the loss.
"It's a tough part of our schedule," noted Pens head coach Michel Therrien. "You knew this was going to be a tough game, and it was. We were not good in every department. Five-on-five, penalty kill or power play. The energy was not there and when the energy is not there, neither is the concentration."
Despite a 9-2 win home win over the Islanders on Thursday, the Penguins were sunk when the Flyers tallied three times in the second period.
Staal redirected a lead pass from Alex Goligoski 7:08 in to cut the Pens' deficit to 2-1, but a Richards wrister off the far post put the Flyers back up by two at 10:09.
Hartnell finished off a quick passing play between Carter and Matt Carle at 12:38 then Knuble added a second power-play goal off a deflection with 2:56 to play for a 5-1 score.
Godard dented Biron on a deflection of Petr Sykora's pass with 8:54left in the contest to bring the Pens within 5-2, then Carter's deflection of Lupul's left-circle shot with 4:10 to go created a four-goal edge.
Fedotenko's wrister under the crossbar on the man advantage with 1:35 to play capped the scoring.
"We wanted a better effort. These are big games in the standings," said Penguins captain Sidney Crosby. "We always should be ready. We knew they had a strong power play, we wanted to stay out of the box. We got into some trouble early and never really got out of it."
The Flyers got on the board courtesy of the power play 5:49 into the contest. Timonen blasted a shot wide from the right wing. Lupul picked up the puck off the left boards and snuck a shot inside the left post and off a Pittsburgh players' skate.
Knuble followed the rebound of a Richards chance from the slot for another man-advantage goal with 8:19 left in the first period.
"There's no question that the fact we won that game made a huge difference with our team," said Flyers head coach John Stevens about the carry-over emotion from the club's comeback 6-5 shootout win over Carolina on Thursday. "The mood was terrific. We had energy which I'm not sure would have been the case had we not come back and won the game."
It was the first time since October 28 that Philly scored at least six goals in regulation...Hartnell's goal was his fourth in two games and the 10th of the season, giving the Flyers five players scoring in double-digits this year...Pittsburgh had won five of the last six regular-season matchups, and both this season entering Saturday...Prior to the game, the Penguins recalled forward Connor James from Wilkes-Barre/Scranton...The Flyers went 4-for-6 on the power play, and the Penguins went 1-for-4.