Lack faced only three shots on goal in the third period and notched his third shutout of the season.
Jannik Hansen scored the only goal of the game at 11:13 of the third period on an assist by Tom Sestito.
The win got the Canucks off on the right foot after the stumbled into the long Olympics hiatus riding a seven-game losing streak.
The loss spoiled a fine start by St. Louis goalie Jaroslav Halak, who stopped 34-of-35 shots.
Neither team scored on a combined seven power plays.