Crosby gave Pittsburgh a 1-0 lead at 5:04 of the second period. After the puck slipped away from Letang as he was battling Shayne Gostisbehere, Hart missed on a poke-check, and Crosby shot through the five-hole.
Crosby had given his stick to Brian Dumoulin in the Penguins zone. When Letang took the puck the other way, Crosby rushed to the bench for a new stick before skating in behind Letang for his 17th goal.
"We have a great crew," Letang said. "Obviously, sometimes if the goalie has an equipment problem or a player breaks his stick, we have a crew that's fast-acting guys. On that play, they were quick to figure out that Sid lost his stick and they did a good job giving him one for the goal."
The Flyers nearly tied it later in the second. After Jarry fell and pinned a shot from Travis Konecny against the left post at 14:54, each of the five Penguins skaters converged on the crease. The puck slipped out, and Couturier tapped it to Justin Braun, but Cody Ceci blocked Braun's shot from the right hash marks.
Jeff Carter was minus-1 with two shots on goal in 17:54 in his Pittsburgh debut. The forward was acquired in a trade from the Los Angeles Kings on Monday.
"I think in the first period, I felt like I was kind of standing still, thinking about the system and trying to figure out where I was supposed to go," said Carter, who was the center on the second line with Jason Zucker and Jared McCann. "The second period, I just started to play hockey. … It's something to build on, for sure."
NOTES: Flyers forward Nolan Patrick left the game at 3:14 of the third period after taking a puck to the face off the stick of teammate Philippe Myers. Vigneault said Patrick told him after the game that he was fine. … Philadelphia forward Wade Allison was minus-1 with four shots on goal in 11:13 in his NHL debut. ... Crosby's goal was his 46th in 75 games against the Flyers, moving past Mike Gartner for the third-most goals scored against Philadelphia, behind Mario Lemieux (51 goals in 71 games) and Jaromir Jagr (47 in 101 games).