Semyon Varlamov stopped 34 shots for his third shutout of the season and the 11th of his career.
Pekka Rinne had 23 saves for Nashville, which has lost two straight.
Barrie scored when he came down the right side and knocked in Greg Zanon's rebound past Rinne. It was Barrie's second goal of the season and ended a four-game skid for the Avalanche.
P.A. Parenteau had his team-leading 21st assist on the play.
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