"Those are big points for us," Barrie said. "We have two games left and we know what's on the line."
John Mitchell scored into an empty net to seal it for Colorado, which is 8-0-1 in its last nine. The Blues, who have lost four straight, and Avalanche each have 111 points with two games left -- but Colorado holds the tiebreaker.
The Avalanche tied a franchise record with 52 wins and Varlamov broke current coach Patrick Roy's mark of 40 wins in a season with Colorado after collecting his 41st of the campaign.
"The coach is very happy," Roy deadpanned.
Barrie's winner came with 7:30 left in regulation with the game tied at 2 and the teams playing 4-on-4. The 22-year-old defenseman moved in on a 2-on-1 rush, toe-dragged around a sprawling Alexander Edler and scored his 13th of the season, and fifth game-winner, past a helpless Jacob Markstrom.
"We hung Markstrom out to dry," Vancouver's Ryan Kesler. "He played good for us tonight and a couple of those goals we hung him out to dry and he had no chance."
Henrik Sedin and David Booth scored for Vancouver, which got 24 saves from Markstrom in his first start for the Canucks.
Edler had a chance to tie it with just over five minutes to go, but Varlamov made a great glove save on the Canucks defenseman.
"Varly was outstanding like he has been all year," Barrie said, "and these next two games are big."
The Canucks were playing their first game since Trevor Linden was hired as the team's president of hockey operations Wednesday. Linden replaced president and general manager Mike Gillis, who was fired after Vancouver was officially eliminated from postseason contention for the first time in six years following a dismal 3-0 home loss to the Anaheim Ducks on Monday.
"I think it was there. Again, I think it's like a lot of other games when we lose," Sedin said. "Shooting enough pucks to the net, enough chances to win but we're making crucial mistakes in the wrong areas of the ice. That's been something that's been happening all year."
Stastny snapped a 1-1 tie with his second of the night and 25th of the season at 5:21 of the third, burying a rebound off Eric Johnson's shot from the faceoff circle.
Booth tied the game 1:39 later with his ninth of the season, roofing Dan Hamhuis' rebound off the end boards over Varlamov's shoulder from in tight.
Linden, who was shown on the video board before Thursday's opening faceoff and received a nice applause, didn't have to look far to see the kind of success former players can have in management. Avalanche executive vice president of hockey operations Joe Sakic has his team in a battle for top spot in the Central Division, while Roy is in the running for the Jack Adams Trophy for a Colorado team that finished 29th last season.
"We played well, we played hard. It takes us a lot of scoring chances to score a goal," coach John Tortorella said. "That has been a recurring theme throughout the year, but I have no beef with our team as far as how hard they played."
Vancouver opened the scoring when Sedin tipped home his 11th of the season off a point shot from Hamhuis at 13:52.
Tortorella said earlier this week that his young players would get a chance to play with three meaningless games left on the schedule, and a play by Vancouver rookie Niklas Jensen directly led to Colorado's tying goal with 1:21 to go in the period.
Stastny stripped Jensen of the puck at the Avalanche blue line and he raced in alone, snapping his 24th through Markstrom.
"These guys want to play for something," Tortorella said. "They know in a couple days we're done. It's a difficult situation, but it's no excuse no matter where we're at not to finish the season the proper way and we're going to keep on trying to that for the next couple of games here."
Canucks defenseman Kevin Bieksa said after the game that he will represent Canada at the world championships. ... The Canucks will honor former coach and general manager Pat Quinn before Sunday's season finale against the Calgary Flames. ... Canucks defenseman Jason Garrison was a healthy scratch as Vancouver chose to dress rookie Frank Corrado. ... Avalanche forward Matt Duchene remained out with a knee injury.
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