Sakic scored his team-leading 35th goal and added three assists to lead Colorado past Calgary 4-3, snapping the Flames' six-game winning streak. Colorado hasn't missed the NHL playoffs since the 1993-'94 season when the franchise was based in Quebec City. The Avalanche has gone a 13-1-2 tear over the last five weeks that has pulled them to within five points of Calgary in the battle for the eighth and final Western Conference playoff spot.
"It's come together at the right time and the guys are playing well, playing hard, we're enjoying this streak right now," Sakic said. "Then again, we know it's still an uphill battle.
"We've got to win all our games and hope that they lose."
Each team has three games remaining, including a head-to-head matchup at the Pepsi Centre on Sunday, the final day of the regular season.
"Joe was great," said Avalanche coach Joel Quenneville. "He's been like that all year, his consistency has been tremendous, his leadership is as great as there is in the game.
"I can't say enough good things about him."
Brett Clark, Brad Richardson and Paul Stastny also scored for Colorado (42-30-7).
Daymond Langkow, Jeff Friesen and Roman Hamrlik replied for Calgary (43-26-10), the NHL's top home team which lost at the Pengrowth Saddledome for just the eighth time (30-8-2).
"We realize that when we've had success, we've had really good starts, we've been able to draw penalties, and we've stayed out of the box," said Calgary captain Jarome Iginla. "Tonight we didn't really do any of those things."
Stastny broke a 2-2 tie and put the Avalanche ahead for good at 14:38 of the second as Colorado took advantage of a lengthy two-man advantage.
Sakic's shot hit Andrew Brunette and went to Stastny, who was alone at the side of the net and scored his 27th goal of the season.
Sakic's goal at 14:41 of the third put the Avalanche up 4-2 and proved to be the winner as Langkow got Calgary to within 4-3 with a power-play goal at 17:21.
Flames left-winger Alex Tanguay tipped his cap to Sakic, his teammate for six seasons up until this year.
"You can't give Joe Sakic time and space like we did," said Tanguay. "We gave him 2-on-1s, a 5-on-3 power-play, you give a guy with that much talent those kinds of chances, it's going to be in the back of your net and that's what happened."
The Avalanche tied it 2-2 at 12:02 when Sakic carried the puck into the Flames zone and centred a pass that Richardson deflected into the top corner.
The Flames led 1-0 at 18:33 of the first, turning a blunder by Budaj into Calgary's 15th short-handed goal of the season.
Budaj couldn't control a 130-foot shot from Robyn Regehr and the puck bounced into the slot where Friesen raced in and fired a slapshot into the top corner.
Sakic credited Budaj for overcoming that moment, noting that longtime teammate Patrick Roy had the ability to forget about bad goals.
"Peter's a great goalie and the best goalies in this league don't worry about a bad goal or a bad game," Sakic said. "I played with one for nine years.
"You're going to have your bad moments and as long as you forget about it and get ready for the next one, you'll be alright."
Still on the power play, Colorado tied it right away on Clark's goal with 12 seconds left in the period.
Budaj finished with 18 saves and is unbeaten in regulation in his last 14 games (12-0-2).
NOTES: Sakic's goal was his 609th of his career, moving him past Dino Ciccarelli into 15th spot on the NHL's all-time list . . . Returning to the Calgary lineup was rookie LW David Moss (six games, lower body) and D Dion Phaneuf (two games, flu) . . . Prior to the game, Rhett Warrener was awarded the Ralph T. Scurfield Humanitarian award in recognition of his community service. It's the second year in a row the Flames defenceman has won the team award . . . Iginla picked up his 338th and 339th assists, moving him past Gary Suter into third spot on the Flames all-time list. Iginla trails Theoren Fleury (460) and Al MacInnis (609).