Nicolas Aube-Kubel scored late in the third period for the Flyers (2-1-0), and Brian Elliott made 13 saves in relief of Carter Hart, who was pulled in the second period after allowing four goals on 22 shots.
The teams will play again in Philadelphia on Tuesday.
"I think if I'm a player, and if I'm part of the coaching staff, which I am, I'm embarrassed by how we played tonight and I'm happy that we can get right back at it tomorrow and prove what type of team we are," Flyers coach Alain Vigneault said.
Lazar gave the Sabres a 1-0 lead at 15:52 of the first period, and then Buffalo's top line took over.
A tripping call on Hart at 2:21 of the second period put the Sabres on the power play, and they took advantage when Hall got the puck to the right of the net, drew two Flyers to him, and passed it through the crease to Reinhart at the bottom of the left face-off circle for a 2-0 lead at 3:35.
"He's a world-class player," Reinhart said of Hall, who has scored six points (one goal, five assists) in his first three games with Buffalo. "I think having everyone that can kind of read and react and play every position (on the power play) is a pretty lethal combo. I think we moved the puck better. ... For him to come and kind of settle the unit down and be able to distribute the puck like that makes a huge difference for us."
Hall and Eichel then set up Reinhart for a goal from the slot to make it 3-0 at 6:28.
Lazar made it 4-0 at 8:09 of the second when Riley Sheahan was first on the rebound of a Brandon Montour shot and passed the puck between his skates through the crease to Lazar at the left post. Elliott replaced Hart after the goal.