Lapierre ended a long scoreless contest by beating Sergei Bobrovsky with a backhander in the third round of the shootout.
Cory Schneider then turned aside Matt Calvert's final try for the Blue Jackets to secure the win.
Schnieder had 17 saves in the contest. Bobrovsky withstood 34 shots in an otherwise stellar performance for Columbus.
The Blue Jackets had only two shots on goal in the first period and was 0-for-2 on their power play opportunities. The Canucks failed to score on their three power plays.