"It feels really good to score goals always," Berglund said, "but at this time of year, it doesn't matter who scores. We just need all the points that we can get here to get into the playoffs."
Anders Nilsson made 21 saves for the Canucks (26-40-9), who are 1-8-0 in the past nine games.
"Tough one," Vancouver coach Travis Green said. "It's 2-1 going into the third, and that first goal in the third, it was a lucky goal, but that's hard to come back from with our team right now against a team that's got some pretty big defensemen. We had a hard time getting inside."
Berglund's goal at 4:44 of the second period was the fifth shorthanded goal of the season for the Blues and made it 2-0. It was Berglund's first multigoal game since March 21, 2017.
Sam Gagner made it 2-1 with his first goal since Jan. 6 (26 games) at 14:47.