Jordan Szwarz also had a goal for the Coyotes, who won for just the second time in five games.
Phoenix has struggled of late, going 3-5-2 in its past 10 games to slip to ninth in the Western Conference. Tuesday's win pulled the Coyotes within a point of Colorado.
Patrick Bordeleau scored his fourth goal of the season and goalie Semyon Varlamov had 22 saves for the Avalanche, who have lost three of their past four. Despite a strong start to the season, Colorado is eighth in the Western Conference.
After a scoreless first half of the game, the goals came quickly. Vermette got the first one when he scored on a give-and-go with defenceman Keith Yandle at 8:31 of the second period.
Szwarz made it 2-0 a little more than three minutes later when he scored on Jeff Halpern's rebound.