Fleury has stopped 95 of 98 shots over this stretch. Pittsburgh controlled the game throughout, allowing few scoring chances to get through to Fleury, who faced six shots in the third period.
"It think it was the easiest shot-wise [of the three shutouts], physically," Fleury said. "Mentally, it's a little tougher because you're not doing anything. You're just standing there, so it's a little tougher to always stay alert, but I thought our guys played so well. They didn't give much."
The Penguins have won their past four games by a combined margin of 19-3. Buffalo has been shut out in five of its first 12 games.
"I just know that I've got to find a way to get this one out of my mind here in the next 15-20 minutes," Sabres defenseman Mike Weber said. "Whether it's been on the road or at home, we somehow have to find an identity to get nasty, get angry. There's not enough anger, there's not enough intensity throughout the game.
"We're not a team that should be pumping the puck in and swinging by guys. We're not a team that gets the puck dumped in on us and it should be easy on their forwards to pick it up and wheel and make plays. Every man has to pick it up."
Chris Kunitz scored his second goal of the game to extend Pittsburgh's lead to four 2:33 into the third while on the power play. It was Kunitz's seventh goal of the season, tying him with Sidney Crosby (three assists) for the Penguins lead.
Crosby leads the NHL with 18 points, three more than Dallas Stars forward Tyler Seguin, Philadelphia Flyers forward Jakub Voracek and teammate Evgeni Malkin.
"I thought we did a pretty good job of holding onto the puck when we had it," Crosby said. "But we just had some trouble early on getting pucks through, they got sticks on them and blocked some shots. So, I think eventually we were able to get more through and get some power plays and capitalize on those."
Malkin scored a power-play goal with 6:49 remaining. He has at least one point in each of Pittsburgh's 10 games after missing training camp because of an undisclosed injury.
The Penguins' NHL-leading power play scored on three of five opportunities. Sabres goalie Jhonas Enroth said he doesn't think he has every faced a power play comparable to Pittsburgh's.
"They have a lot of great tools," Enroth said. "The power-play goals they scored were pretty good goals and hopefully we can take a page from their book and see how a great team plays on the power play."
The puck barely exited the Buffalo zone throughout the first period, with the Penguins entering the intermission holding a 1-0 lead and 12-3 shot advantage.
Kunitz opened the scoring with his sixth goal of the season 4:26 into the first. Crosby drove through defensemen Tyler Myers and Josh Gorges before sliding a shot on goal. Patric Hornqvist whacked at the rebound off of Enroth's pads and the puck jumped to Kunitz, who wristed it into the net.
Buffalo recorded the game's first shot 57 seconds into the game, but went 13:06 without another.
Pittsburgh added two second-period goals to take a 3-0 lead into the third period, despite the Sabres playing a more fluid style that led to nine shots. Blake Comeau extended the Penguins' lead to 2-0 with his third goal of the season 11:54 into the second.
Malkin stopped by the right boards inside the blue line and slid a pass to Comeau, who was darting through the middle. Comeau sent a shot past defenseman Andre Benoit, who went to his knees and turned sideways, and Enroth's outstretched glove.
Malkin earned another assist when he helped set up Hornqvist's power-play goal with 3:51 remaining in the second. Malkin found Kunitz to start a tic-tac-toe series of passes before the puck came to Hornqvist, who one-timed a shot past Enroth.
The goal came after the Sabres were called for too many men on the ice, which nullified a hooking call on Crosby. Buffalo, which has scored one power-play goal this season, failed to score on four opportunities.
"It's the same recipe and the same results," Sabres coach Ted Nolan said. "It's 1-0, we had a little bit of pressure in the second period, then we have a turnover and it's [2-0], then we take a penalty and then the game's over. The confidence factor right now, if we get down by two goals, it doesn't seem like we have the will to battle back."
The Penguins have killed 26 consecutive penalties. Penguins coach Mike Johnston credited Fleury with part of that success.
"You have a feeling that your goaltender is in the zone, so we went back to him tonight," Johnston said. "We weren't really sure what we were going to do this week for the rotation of the goaltenders. … But he was good in Nashville [last Saturday] and he continued right through this week off the road trip, so you can't say enough about having a goaltender that will play like that.
"Especially on the power-play pressure. They had a few good shots on the point that he had to find on the power play and I thought he did a really good job around the crease."