After Tyler Ennis opened the scoring early in the second period with his first goal of the season, Matt Moulson scored twice on the power play to give the Sabres a 3-0 lead heading into the third period. Nilsson made 38 saves in his first start for Buffalo (1-2-2).
"It's on us to be better," Sabres captain Brian Gionta said. "We showed we could take over the game and make something happen. It's tough. We need to find a way to go into that third and get a win."
Streit scored with 1:51 remaining to tie the game 3-3, lifting his rebound over a pile of players in front of the net. Sabres coach Dan Bylsma challenged the goal for goaltender interference, but it was upheld by video review.
Konecny tipped an Ivan Provorov shot past Nilsson for his first NHL goal at 4:30 of the third to make it 3-1, and 24 seconds after Kulikov was assessed a charging penalty for his hit on Voracek, Schenn scored with 2:56 remaining to pull Philadelphia within a goal at 3-2.
Moulson's second goal, a one-timer at 15:43 of the second period that chased Neuvirth, gave the Sabres a 3-0 lead. Flyers coach Dave Hakstol challenged the goal for goaltender interference, but it was upheld by video review.
Neuvirth allowed three goals on 17 shots.
Ennis gave the Sabres a 1-0 lead at 2:06 of the second when he tipped a sharp-angled shot by Zemgus Girgensons past Neuvirth, and then Moulson won a race for a loose puck in the Flyers zone and scored on a backhand from in front at 3:56 for a 2-0 Buffalo advantage.