Most of the third period turned out to be a tense goaltending duel, but Stastny broke that up by scoring his first two goals of the season.
The first one came on the power play and the second one followed 1:29 later on a wrist shot. P.A. Parenteau added an empty-net goal with 48 seconds remaining.
Colorado's six-goal outburst came after the Avalanche had managed a league-low 10 goals in their first six games. Colorado snapped a three-game skid.
Ohio crash that killed two caught on camera [VIDEO]
Wisconsin business offering 'therapeutic cuddling' forced to close