Crosby's goal tied him with Jaromir Jagr for second in Penguins history with 439. Mario Lemieux is first with 690.
The Penguins are 5-7 in games decided in overtime this season.
Eichel extended his point streak to seven games when he shot from the left face-off dot and beat Murray to the short side to make it 1-0 at 3:09 of the first period. He has nine points (five goals, four assists) in the streak.
Bjugstad tied it 1-1 56 seconds later from the left circle at 4:05.
Sheary gave the Sabres a 2-1 lead on the power play at 12:53 after Kyle Okposo received a pass from Montour at the goal line and sent the puck to Sheary in the slot.
Pittsburgh outshot Buffalo 20-7 in the first period.
"We probably had more scoring chances, but it's hockey," Penguins center Evgeni Malkin said. "Sometimes that happens. They scored in the final three minutes, we need to help block shots, help the goalie. It's hockey, sometimes it's a little bit of luck."
The Penguins took advantage of a four-minute double minor to take their first lead of the night, scoring twice in 57 seconds. Hornqvist, screening Ullmark, deflected Schultz's point shot at 17:18 to tie it 2-2 at 17:18, and Crosby scored on a one-timer from the right circle for a second power-play goal at 18:21.
"Whenever you put a team like that on the power play for as much as we did in the second, for one, I think it ruins the flow of the game," said Eichel, the Buffalo captain. "And two, you're giving their best players a lot of touches and they're getting into the game and starting to feel themselves. So it's never easy. I know if you're on that opposite side and you're getting all those power plays, your game starts coming because you're feeling the puck a lot. I thought we did a good job coming out in the third and finding a way."
