David Jones, who had scored one goal in the previous 15 games, redirected Tomas Fleischmann's pass on a 2-on-1 rush by goalie Ryan Miller with 42.9 seconds remaining in the extra period to put a halt to the Avalanche's home losing skid at four games.
"We have a big stretch here at home, and we need to win games here in front of our crowd," Jones said. "We haven't been doing that, so it's nice to get the monkey off our back. We have to carry the momentum into next game."
Jones' goal came during a 4-on-3 skating advantage with Buffalo's Tyler Ennis in the penalty box for high-sticking Ryan Wilson with 15 seconds left on a tripping penalty to Colorado's Milan Hejduk.
Only five seconds remained on Ennis' penalty when Jones scored after Wilson fed Fleischmann skating down left wing.
"Flash just kind of took the puck wide and the D-man slid there trying to take away the pass and he made a great play just to get it over to me," Jones said.
"The goalie was pretty much playing him, so I pretty much had a wide-open net up top there and I hit the spot. I couldn't be more excited."
Colorado had failed to score on its previous five power plays in the game and on 14 consecutive man advantages covering seven games.
"Flash made a sick pass to Jonesie, and he put it upstairs," said Matt Duchene, who tied the game 3-3 at 6:02 of the third period off a setup from Fleischmann. "I think we've been playing some real good hockey and we found a way to win, so it was great."
The Avalanche, which killed seven of eight penalties, caught a huge break during a Sabres' power play with the score tied 3-3 and 5:35 to play in regulation. Goalie Peter Budaj was on his belly when Luke Adam took a shot that hit Budaj's right skate. The puck would have sailed into the net, but Ennis got his stick on it from the side of the net and inadvertently swatted it back.
A video review confirmed the puck didn't completely cross the goal line, and the Avalanche killed off the remaining 46 seconds of the penalty.
"I just tried to jam the net," Ennis said. "The puck squirted out there. Luke, I saw he had the whole net and the shot came and my stick just happened to be sitting there. For whatever reason, (the puck) decided to hit my stick and doesn't go in. Just really disappointing."
Said Adam: "It was a matter of centimeters. Obviously it wasn't in and they called it no goal. It was pretty close."
The Sabres took their only lead at 3-2 in the third period when Jochen Hecht and Steve Montador scored 63 seconds apart, but Duchene tied the game shortly after Avalanche coach Joe Sacco called a timeout.
"I just told the players that we were mismanaging the game a little," Sacco said.
"We wanted to put the puck deep, and we didn't do that. We started to turn it over and it got a little contagious. They capitalized on a few of our mistakes and
I thought it was the right time to kind of regroup the players and let them know there was still a lot of time left, and Duchene came up with a big timely goal for us."
Winnik beat Miller at 14:16, whipping the puck inside the near post from the right circle off a long pass from TJ Galiardi for a 1-0 lead.
The Sabres countered 33 seconds later when Thomas Vanek tapped the puck in from just outside the crease 12 seconds after Avalanche defenseman Ryan O'Byrne was assessed a double minor for high sticking.
Just over a minute after that, during the second Buffalo power play, Winnik passed to O'Reilly for a one-timer in front to regain Colorado's lead.
The Avalanche, which totaled 10 goals during a 1-4-1 slump before Tuesday, played without center Paul Stastny, a late scratch because of flu-like symptoms.
1 - 0 COL
1 - 1 Tie
2 - 1 COL
2 - 2 Tie
3 - 2 BUF
3 - 3 Tie
4 - 3 COL
Hi stick - double minor