Victor Olofsson scored twice, Tage Thompson had a goal and an assist and Owen Power, Rasmus Dahlin and Jeff Skinner each had two assists as Buffalo (7-3-0) has won three games in a row.
"We know they've got a lot of skilled players", Alex Tuch said. "We didn't get down on ourselves, we didn't slump down and we went out there and tried to respond right away. We were able to have a great come-from-behind win there, and it showed a lot of guts in this room.
"It took all of us, honestly. We all beared down and it started with 'Coms' in net and went out from there. So, a lot of guys stepped up in that third period and we responded well."
Evgeni Malkin had two assists and Casey DeSmith made 27 saves as the Penguins (4-5-2) slumped to a sixth defeat in a row.
"You've got to build confidence", said Pittsburgh captain Sidney Crosby. "There's no secret. In a situation like this, it just comes down to finding your way and being determined. It's work and finding a way to get out of it. We can't sit around and feel sorry for ourselves".
Sabres rally to deal Penguins sixth consecutive defeat
Pittsburgh took the lead 6:28 into the game, Malkin sending a pass to Jason Zucker in a two-on-one and he beat Comrie from the right face-off circle.
The lead was extended to 2-0 when Ryan Poehling fed Josh Archibald on another two-on-one. Archibald scored for the second straight game.
J.J. Peterka made it a 2-1 game with 1:09 left in the second period after taking a pass from Power at the half-wall and skating to the right circle.
Eight seconds into the third, Jake Guentzel restored Pittsburgh's two-goal lead, Kris Letang sending a stretch pass to him from inside his own blue line while on the power play.
"That first part of the game, I thought we did a pretty good job of just creating offense off of defense", Penguins coach Mike Sullivan. "We got a number of two-on-ones, odd-man rushes by just defending hard and making good decisions, winning the wall battles, getting pucks behind their defensman and getting in foot races. And then I thought the third period or second part of the game, we just didn't do as good a job at beating the pressure on the walls and just recognizing danger and just making simple plays."
Thompson made it a one-goal game again with a one-timer from the left circle on the power play and after a fake shot-pass from Power, Olofsson was left uncovered and tied the game with 13:31 left.
"Like everyone else, I thought he was going to shoot it at first", Olofsson said. "But I was ready for it. It was a nice fake pass and fake shot and incredible pass."
Tuch drove to the net and redirected a pass from Thompson to give the Sabres their first lead of the night at 4-3.
"To give up the goal immediately to fall down two goals, we hadn't had a good night to that point yet, and then we responded", Buffalo coach Don Granato said. "So, it's a testament to the group's will, determination. But I think they also, they know and we know their identity, and we knew we weren't playing to it to that point. I think the collective feel going into the third (was), 'We are going to get to that, and we are going to turn it up'".
Kyle Okposo and Olofsson added empty-net goals for the 6-3 final.
It was the first time the Sabres scored five goals in the third period of a game since a 6-3 win at Boston on Dec. 26, 2015.
"[The mood in the room is] what you'd expect for a team that's blown a couple of leads on back-to-back nights and winless in six", Crosby said. "I mean, it's not a great feeling and we've got to find a way to get out of it."