Hejduk, playing in his 900th career game, scored on a wrist shot that capped an Avalanche comeback that included two goals by Matt Duchene and a tying goal by Daniel Winnik with 3.3 seconds left in regulation.
Brian Elliott made 29 saves in goal for Colorado and stopped all three shootout tries by the Blue Jackets.
Columbus goaltender Steve Mason made 28 saves.
The win snapped an eight-game Colorado home losing streak and gave the Avs their first back-to-back victories since mid-January.
R.J. Umberger had two goals for Columbus, including one of the Jackets' two short-handed scores.
Columbus lost for the fourth time in five games.
Swim Week Miami Beach 2014 [PHOTOS]