The Sabres found themselves in an early hole, trailing 3-0 in the first period. Gabriel Landeskog put the Avalanche up 1-0 just 2:06 into the game and his goal was followed by ones from Mikhail Grigorenko and Tyson Barrie later in the period.
After the third Colorado goal with 5:36 remaining, Sabres coach Dan Bylsma called a timeout.
"The timeout was really [to] reset, refocus," Bylsma said. "Coming off the break, we knew it was going to be a tough game for us. It's just disappointing we give them three off the hop and we have to reset and try to get back to playing our game and focus on coming back in that game."
The Sabres were able to collect themselves, scoring on the power play a few minutes later and adding another midway through the second to make it a one-goal game.
"His message was, we still had a good part of the game to get ourselves back in it. We weren't that far off and we go down 3-0," captain Brian Gionta said. "No matter who it is, it's going to be tough coming back. We had a good effort in that, but it just wasn't good enough at this time."
Buffalo had some quality chances early on, but just weren't able to capitalize. They ended up outshooting Colorado 37-30.
"It wasn't a terrible start by any means," Gionta said. "We had some sustained shifts within that first 10 minutes or so, but the breakdowns that led to the goals - just like that, everything kind of snowballed and went in against us."
Sam Reinhart, Marcus Foligno and Evan Rodrigues scored for Buffalo. Robin Lehner made 25 saves in net.
Jeremy Smith, in his third career game, picked up the first win of his career for Colorado.
Buffalo was quick and precise on Reinhart's goal, which was scored six seconds into the man advantage to make it 3-1 with 2:49 remaining in the first. Ryan O'Reilly won the faceoff back to Ristolainen at the right point who sent it over to Jack Eichel on the left wing.
Eichel fired a shot on net and Reinhart buried the rebound for his 14th goal of the season and his ninth of the year on the power play.