The Flyers, who equaled a franchise record with their 25th road victory, also have home games against the Rangers and Buffalo. Pittsburgh's other two games are at Boston and against the Rangers.
The Flyers and Pens are headed toward a first-round matchup, and bad blood is brewing. With 1:03 left, there were several skirmishes, and Flyers coach Peter Laviolette and assistant Craig Berube screamed at the Penguins' coaches, particularly assistant Tony Granato, after Pittsburgh's Deryk Engelland decisioned Simmonds in the main bout.
Laviolette and Granato were ejected.
The scrums started after Pittsburgh's Joe Vitale crunched Danny Briere with an open-ice hit.
The Flyers are 5-0 at Consol since it opened two years ago, with goalie Sergei Bobrovsky (43 saves on Sunday) winning all five games. For the second straight game, the goalie settled into a groove after a rocky start.
For the Flyers, all the news wasn't positive. They lost the services of 6-3, 230-pound Nick Grossmann, their most physical defenseman, with an apparent knee injury. Grossmann collided, knee on knee, with Vitale and went to the locker room with 8:25 left in the first. He did not return.
Without Grossmann, who had been paired on the team's shutdown unit with Braydon Coburn, the Flyers had to double-shift most of their defensemen.
Trailing 2-1, former Penguin Max Talbot tied the score 1:25 into the second period, redirecting a shot taken by Zac Rinaldo.
Simmonds, after a great feed from Jakub Voracek, gave the Flyers a 3-2 lead by slamming home a goal from the doorstep while the Flyers were on a power play with 17:25 left in the third.
About four minutes later, Voracek sped past the Penguins' defense and scored on a breakaway, increasing the lead to 5-2. Marc-Andre Bourdon made it 5-2 when his long shot deflected off defenseman Zbynek Michalek and past goalie Marc-Andre Fleury with 6:45 to play.
Steve Sulliavan's second goal of the game cu the Flyers' lead to 5-3 with 4:42 remaining.
Voracek locked up the win with an empty-netter.
For the sixth time in the last nine games, the Flyers faced a 2-0 deficit. Sullivan and James Neal scored in the first 4:58 as Pittsburgh took control. Sullivan scored on a blooper of a shot from the slot; the puck appeared to be deflected in front and it fluttered high into the net at 1:14.
Sidney Crosby assisted on the goal, giving him 18 points in 11 games since returning from an injury on March 15. It also gave him 49 points in the last 30 regular-season games against the Flyers.
The Flyers have allowed the first goal in seven of their last nine games.
Shortly after Sullivan's goal, Flyers defenseman Matt Carle fired a shot off the post.
Neal, left alone in front, made it 2-0 by converting a pass from Evgeni Malkin. Neal got position on backchecking Scott Hartnell.
With Hartnell battling Michalek in front and distracting Fleury, the Flyers got to within 2-1 as Claude Giroux's shot from inside the blue line found its way into the net. It was just Giroux's second goal in nine games - and only the second goal by a member of the Flyers' top line in the last five contests.
Getting home ice "is important because in a seven-game series, Game 7 is at home," Talbot said before the game. "The momentum changes from game to game," but you want to have Game 7 on home ice.
The Flyers are 4-1 against the Penguins this season. In the teams' March 18 game, the Flyers overcame a 2-0 deficit and scored a 3-2 overtime win on Hartnell's goal with 0.9 seconds left.
Contact Sam Carchidi at firstname.lastname@example.org or on Twitter @BroadStBull.