Varlamov came up big in the third period with the Avalanche clinging to a one-goal lead, turning aside all 17 Dallas tries to secure Colorado's sixth win in six games beginning the season.
Duchene's first goal -- an unassisted tally midway through the first period -- forged a 1-1 deadlock, and his second score late in the middle period put the Avs ahead to stay at 3-2.
Cody Eakin and Rich Peverley scored for the Stars.
Dan Ellis stopped 23-of-26 shots in the loss.
Exploding whale video goes viral on Internet
Sign language interpreter at Mandela service called out as fake on Twitter