On the decisive play, Colorado defenseman Jan Hejda kept the puck in the Boston zone at the left point and sent a pass along the boards to Hejduk.
The veteran Avs forward then skated into the circle and flicked a wrist shot that got through the pads of Bruins goalie Tuukka Rask with 7:57 remaining in the contest.
Semyon Varlamov held on to notch his fifth career shutout, stopping all 30 shots he faced and recording his first victory as a member of the Avalanche. The former Washington Capitalsgoalie went to Colorado in an off-season trade.
Rask turned aside 35-of-36 shots for the Bruins, who dropped their seventh straight home game to the Avalanche.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys