The two teams had entered the third period with one goal apiece, but the Ducks scored three straight goals to build their lead.
"Going to a third period 1-1, we've got to expect more out of ourselves going in this stage of the season," said Sabres goalie Robin Lehner, who made 39 saves. "That stage of the game, a 1-1 hockey game, we didn't have a push. They had a push."
The push began 55 seconds into the period thanks to Perry's playmaking skills on the rush, when he cut to the middle to draw the defense and then fed Rickard Rakell for his 22nd goal. He notched his own goal later in the period on the rush as well, this time burying a rebound off of a Rakell shot.
Perry had already scored Anaheim's first goal with 2.4 seconds remaining in the first period.
"I just think we turned too many pucks over against a good team with a lot of good forwards," said forward Jack Eichel, who scored on the power play in the second period. "We didn't contain their speed at all through the neutral zone and the puck ended up in the back of our net."
Sandwiched between Rakell and Perry's third-period scores was a tipped goal from Antoine Vermette on the power play, which came after Ryan O'Reilly received a double minor penalty for high-sticking Ryan Getzlaf on a faceoff.
The shots overall were 44-26 in favor of the Ducks, marking the ninth straight game that the Sabres have allowed 35 shots or more to their opponent.
"It's just about stacking the odds against you," Lehner said. "When we get it down a little bit and take away the middle and take away some quality chances, that tip, maybe it' not happening, that bounce. The more chances, the more opportunities for a bad bounce. We need to clog up the middle, I don't know. I'm sure coach is going to walk us through it but we've got to definitely step up."
"We've been playing against pretty good teams like tonight and a couple nights ago, but still we've got to help out our goalie more," Ristolainen added. "They've been huge for us. Somehow, we've got to play tighter, have better gaps. Maybe, I would say, more shot blocks too."
Eichel said he thought the Sabres were too loose when possessing the puck, and Dan Bylsma pointed to lopsided possession time as the cause for the lopsided shot totals.
"Tonight I think through two periods their defensemen had 14 or 15 attempts on net," the Sabres coach said. "That's an offensive zone indicator of having possession of the puck and having it in the offensive zone and going low to high and getting shots on the cage. That's been really a common denominator."
In their game on Tuesday, the Sabres were able to get away with allowing that kind of offense thanks to a memorable third-period run. Lehner's point on Thursday was that the team can't keep expecting to rely on such comebacks.
"Comeback victories, [they're a] great momentum boost or moral boost or whatever," the goalie said. "But comeback victories, they're called comebacks because we've put us in a hole. It's not all the time going to bounce that way."