Dylan Cozens and Kyle Okposo each had a goal and an assist, and Dustin Tokarski made 18 saves for the Sabres (16-29-8), who have lost five in a row outscored 24-10.
"We controlled a lot of the game," Okposo said. "That's just a good group over there. They've got a lot of guys who've been around a long time and they just stuck with their plan and they weathered the storm. They bent and didn't break, and we just gave them a couple too many chances and they capitalized on them. But I thought that we were a better team for the majority of [the game]."
Tage Thompson's power-play goal for Buffalo tied it 3-3 at 12:34 of the third period. His wrist shot from the slot beat Husso high glove.
"It's always nice to score," Thompson said, "but I think the main thing is winning. I really wanted to win this one, and everyone in the room did too, and it stings a little bit more, especially when you play well like that. And that's a tough one as well."
Colton Parayko gave the Blues a 4-3 lead at 13:57 when he followed Kyrou's shot off a 2-on-1.
"He's the fastest skater, he's obviously got good speed and obviously good play by him," Parayko said. "Obviously he had a really good game, but he's a fast guy, tough to keep up with for sure.
"I was just kind of driving back post, kind of ready for a pass if we had an opening, or else just kind of go backdoor maybe if there was a rebound like there was. Just kind of drive the net and make it hard on that defenseman too, to take away the pass and the shot at the same time, kind of. Just being a D-man, I know how hard it is. When guys are pushing backdoor, you've got to kind of commit to something. Nothing overly exciting, just making sure I was driving that back post making it tough on that D-man."