Tyler Seguin and Jason Robertson each had two goals and an assist, Roope Hintz had a goal and an assist, and John Klingberg had four assists for the Stars (19-16-2), who had lost three in a row. Braden Holtby made 20 saves.
Rasmus Dahlin had a goal and two assists, and Jack Quinn scored his first NHL goal and had an assist for the Sabres (12-21-7), who lost for the second time in three games after entering the third period with a lead. Aaron Dell made 42 saves.
"I feel like they came out pretty slow," Dahlin said. "We took advantage of it. We scored a couple goals there. But then the second and the third period, they did the right things over and over again and they rolled over us. Our young guys did a great job today, but we just have to find a way to win these type of games against this type of veteran team. It [stinks], for sure."
Seguin tied it 4-4 at 12:23 of the third period, taking a cross-ice pass from Hintz and scoring a power-play goal from the right circle.
Robertson gave Dallas a 5-4 lead at 16:28 when he batted in his second goal on the man-advantage.
"I felt pretty good out there," said Robertson, who returned after missing two games with a lower-body injury. "I was fortunate to have my teammates having my back out there if I made any turnovers or mistakes or anything. So it's good to have them behind me. And I think on that line with Joe [Pavelski] and Roope, it's hard not to get your feet going. Everything happens so fast."
Dahlin gave Buffalo a 1-0 lead at 2:47 of the first period. He took a drop pass at the right point, got around Joel Kiviranta, and drove to the net before scoring with a backhand past Holtby's outstretched left pad.
Quinn, who was selected with the No. 8 pick in the 2020 NHL Draft, made it 2-0 with a power-play goal at 6:37. Dahlin chipped a pass through his legs to Quinn, who skated to the right circle and shot glove side.
"Something you kind of dream about," Quinn said. "So it was pretty special to see it go in and it was exciting to celebrate with my teammates there."