What are the odds that three Avalanche players will be sidelined with back problems in a span of a few days? What are the odds of the Avalanche getting outshot 48-26 in Chicago and leaving the United Center with a win?

Thanks to the superb goaltending of Semyon Varlamov and another big game from defenseman Tyson Barrie, the Avalanche pulled out a 3-2 overtime win against the Blackhawks on Tuesday night to complete a sweep of the two-game road trip and solidify the team’s third-place standing in the Central Division.

The Avalanche has a 29-12-5 record and 63 points in 46 games. Fourth-place Minnesota has 55 points in 49 games and fifth-place Dallas has 49 points in 46 games.

Varlamov made 46 saves and Barrie, who had two goals, scored on a power play with 50.7 seconds left in overtime for his second OT goal in a week.

“He’s been like this since the start of the year,” coach Patrick Roy, speaking to reporters, said of Varlamov. “He’s been outstanding. We rally around him and that was the type of performance we needed from our goalie to beat the Blackhawks.”

Said Barrie: “This is huge for us. This is a tough building to get one point in, so we got that one and we were fortunate to get a power play there and it was nice to capitalize on that and get the two points.”

Chicago’s Jonathan Toews was in the penalty box for hooking defenseman Andre Benoit when Barrie scored.

Ryan O’Reilly, who scored twice Saturday in the Avalanche’s 4-2 win in Minnesota, collected a power-play goal Tuesday to take over the team goal-scoring lead with 17, one fewer than the career high he had in 81 games in 2011-12.

The Avalanche went 2-for-4 on power plays and killed all five of the Blackhawks’ man advantages, during which Varlamov made 13 saves.

The Avalanche started the game with 11 forwards — Paul Stastny hurt his leg Saturday and didn’t dress — and six defensemen, with Nick Holden getting some time at left wing on the fourth line. Defenseman Cory Sarich was expected to play, but he was a late scratch because of a back ailment and defenseman Erik Johnson managed to take one brief shift in the third period before calling it a night because of his back injury.

Goalie Jean-Sebastien Giguere already was sidelined because of back spasms, which is why Sami Aittokallio was called up from Lake Erie of the AHL to suit up as Varlamov’s backup.

Defenseman Nate Guenin (ankle) and forward David Van Der Gulik (on injured reserve with a head injury) were scratched, along with Stastny and forwards PA Parenteau (knee) and Alex Tanguay (knee, hip).

In terms of puck possession and territorial edge, the game was even more one-sided than the shots total. The Avalanche blocked 23 shots and the Blackhawks missed the net on 17 attempts, bringing Chicago’s shots on goal and attempts up to 88. The Avalanche had a total of 37 shots and attempts, with eight blocked and three that missed the net.

Varlamov has gone 9-0-5 in his past 15 games (14 starts) and permitted two goals or fewer in 10 of them. He’s won five of eight career decisions against Chicago and his 22 wins this season are four shy of the career high he set in 2011-12, his first year in Colorado.

Matt Duchene failed to score a goal for the 12th consecutive game, but he made the pass to set up Barrie’s winning goal. Barrie opened the scoring by using Patrick Bordeleau as a screen to beat goalie Corey Crawford with a long shot that went just inside the right post.

Avalanche defensemen had to log plenty of minutes: Holden played a team-high 25:11, followed by Benoit (24:26), Jan Hejda (23:08), Barrie (23:05), Ryan Wilson (18:09) and Johnson (limited to 12:45 because of his back problem).

Now 13-6-2 in road games and on a 6-1-2 roll in the past nine games overall, the Avalanche returns home to face the New Jersey Devils on Thursday.