The Flyers got goals from Danny Briere, Blair Betts, and Claude Giroux.
Briere, stationed to the right of the net, redirected Mike Richards' deft pass from the point past goalie Marc-Andre Fleury's glove on the short side with 17 minutes left in the second period. The power-play goal, the first score in the new arena, gave the Flyers a 1-0 lead.
"A few years ago, my first two years with the Flyers, I was used to having Richie back on the point on the power play," Briere said. "We scored a few goals like that. . . . When we won the face-off and he got the puck, all I was thinking was to find the open space by the side of the net.
"Richie found me just like the good old days, I guess."
With 2 minutes, 45 seconds left in the second period, Darroll Powe tipped James van Riemsdyk's shot off Fleury, and Betts knocked in the rebound to put the Flyers ahead by two, 2-0.
Forty-four seconds into the third period, however, the sellout crowd erupted as Tyler Kennedy, from a bad angle near the top of the left circle, beat Bobrovsky to cut the Penguins' deficit to 2-1.
The Penguins, on the power play, nearly tied it with about 16½ minutes left, but Sidney Crosby's shot caromed off the post - the fourth time Pittsburgh hit iron in the game.
During the same power play, Giroux made the play of the night, stealing the puck from defenseman Kris Letang and scoring a shorthanded goal on some dazzling breakaway moves. His forehand-backhand-forehand maneuver faked Fleury and gave the Flyers a 3-1 lead with 15:05 remaining in regulation.
Nineteen seconds after Giroux's goal, Pittsburgh got to within a goal, at 3-2, when defenseman Alex Goligoski scored on a point drive with one second left on the power play. The shot may have deflected off Flyers defenseman Braydon Coburn.
The Flyers, now 20-16-7 in openers in their history, downplayed Laviolete's decision to start Bobrovsky over veteran Brian Boucher.