With the Blues on a power-play, Alex Pietrangelo threaded his way down the left side, moved toward the net and found Berglund open on the other side of the crease for a tap-in and a 3-1 St. Louis lead.
The goal proved decisive when Jannik Hansen pulled the Canucks to within a goal with 1:47 remaining in the game, but Vancouver could come no closer and the Blues hung on to win for only the third time in 10 games.
Alex Steen and Andy McDonald also scored and Jaroslav Halak stopped 23-of-25 shots for St. Louis.
Henrik Sedin scored and Roberto Luongo absorbed his first regulation-time loss since Dec. 5, a span of 22 games, finishing with 31 saves for the Canucks.
Celebrity Families of 2014 [PHOTOS]