Trailing 3-2 after Jason Garrison's goal gave Vancouver the lead early in the final frame, the Avalanche got the equalizer with 7 minutes to go when P.A. Parenteau notched his 16th goal of the season.
Then, with an extra attacker on the ice as time was running down, Colorado pulled out the victory when Hejda's slap shot found its way past Canucks goalie Cory Schneider.
Gabriel Landeskog and Cody McLeod also tallied for the Avs, who improved to 2-4-2 in April.
Jean-Sebastien Giguere made 24 saves in the victory.
2014: The Year in Music [PHOTOS]