Thanks to Jamie McGinn scoring with two seconds remaining in regulation and Colorado's near-perfect shootout record this season, the Avalanche went from losing ground in Western Conference playoff hunt to vaulting out of a four-team log-jam for eighth place.
"This is the biggest win of the year," Mueller said. "To go from zero points to getting two with seconds left, you don't make that stuff up. It just shows the character of this team in that we never quit."
McGinn, who scored twice, was equally pleased.
"We knew how important this game was to stay in the hunt," McGinn said. "And we got the job done."
It was a different story for the Sabres, who lamented how costly the lost point in the standings might affect their late-season playoff push. Buffalo (33-29-9) is three points behind eighth-place Washington in the East.
"Frustrating," coach Lindy Ruff said. "You play with fire, you'll get burnt. We should have had a D in front of the net, and one of the defensemen were behind the net."
Ruff was referring to McGinn's tying goal, which came during a wild scramble in front.
Gabriel Landeskog gained the zone and got a shot off that Ryan Miller stopped with his blocker. The puck eventually went to the right corner, where Ryan O'Reilly took a bad-angle shot that sneaked between Miller's pad and the post. The puck trickled into the crease, and McGinn swept it in.
It was reminiscent of the Sabres' 3-2 overtime win over Montreal on Monday night in which Buffalo allowed the Canadiens to tie it with 5 seconds remaining.
Only this time, the Sabres lost.
Mueller's decisive shootout goal came on the Avalanche's second attempt. He snapped a shot that beat Miller on the glove side. Semyon Varlamov then secured the victory by stopping Tyler Ennis' drive to the net.
"I jumped in the air like we won the Stanley Cup," Varlamov said. "It was huge. We never gave up."
Varlamov made 20 saves through overtime, and improved to 8-0 in the tiebreaker. Landeskog had a goal and assist, and David Jones scored for the Avalanche (38-30-4), who improved to 9-1 in shootouts this season, and 20-2 since December 2009.
Rookie Marcus Foligno scored twice for Buffalo, which had a season-best five-game home winning streak snapped. Drew Stafford had a goal and two assists, Ennis had three assists, and Alexander Sulzer also scored for the Sabres.
"We just have to be in desperation mode at all times," said Miller, who made 38 saves. "Four goals should win. They got a couple of fortunate bounces."
The loss spoiled a big night for Foligno, who scored twice with his father -- former Sabres captain Mike Foligno -- in the stands.
Fans initially thought he had scored a third goal, and littered the ice with hats in the third period. But the goal that put Buffalo ahead 4-3 was credited to Sulzer, as replays showed the puck went off the stick of Colorado defenseman Matt Hunwick, and not Foligno.
Foligno gave the crowd a big reason to cheer when he scored his first of the game 1:39 in. He slipped in front, while attempting to handle Ennis' centering pass, and the puck caromed off his skate and Jones' skate.
Upon scoring, Foligno jumped up and down once, mimicking his father's goal celebration.
"It was good effort by us, but in the end it was a tough pill to swallow," Foligno said.
It was a back-and-forth game with the Sabres squandering two one-goal leads in the first period. Landeskog put the Avalanche ahead 3-2 with a power-play goal 5:35 into the second period. Foligno then tied it less than six minutes later.
- Sabres D Tyler Myers began serving a three-game NHL suspension for a hit against Montreal on Monday.
- With Andrej Sekera (pneumonia) missing his fifth game, the Sabres recalled rookie Brayden McNabb from AHL Rochester. McNabb had a goal and four assists in 20 games with Buffalo earlier this season.
- The Avalanche opened a three-game road trip, and in the midst of a 16 games in 30-day stretch.
- Sabres C Nathan Gerbe didn't play due to an undisclosed upper body injury. Cody McCormick took his spot, returning to the lineup after missing 16 games with a concussion.
- With speculation that NFL free-agent DE Mario Williams was in attendance, fans chanted "We want Mario!" Williams has spent two days negotiating with the Bills.