Colaiacovo's wrist shot from just inside the blue line deflected off Colorado's Gabriel Landeskog, causing it to change direction and fool Avalanche goalie Semyon Varlamov.
The Blues used the victory to extend their franchise-record home point streak to 18 games (15-0-3).
Brian Elliott earned the win with 17 saves.
Varlamov turned aside 41 shots but it wasn't enough to prevent the second overtime loss in four games for the Avalanche.
Notable deaths of 2014 [PHOTOS]