The Avalanche twice came back from a one-goal deficit and then moved in front for the first time on Talbot's fourth goal of the season. Matt Duchene added an empty-net goal with two seconds to play.
Semyon Varlamov blanked the Oilers during the final period and finished with 26 saves to get the win.
Edmonton, with a conference low 11 victories for the season, lost its fifth in a row.
Devan Dubnyk stopped 35 shots.