Barrie scored twice Tuesday, including the first goal of the game and then the winner on a power-play with 50.7 seconds left in overtime off a backhanded pass from Matt Duchene.
Barrie's goal was one of two power-play scores for the Avalanche, who improved to 6-1-1 in their last eight games. Semyon Varlamov was solid in goal with 48 saves, including four in OT.
Corey Crawford turned in 23 saves for the Blackhawks, who have one win in their last five games. Johnny Oduya and Andrew Shaw scored Chicago's goals in the second and third periods to forge a 2-2 tie and force overtime.