Brian Elliott made 21 saves in regulation and stopped Derek Roy and Alexandre Burrows in the shootout, solidifying the Blues' chances in a tight Western Conference race. Bowmeester's goal was his first since joining the Blues in a trade-deadline deal.
Alexander Edler scored on a power play late in the second period for Vancouver. Cory Schneider made 35 saves in regulation but surrendered two goals on three shootout chances.
The Canucks played for the third time in four nights, all on the road, and had trouble generating much offence coming off a 5-2 victory at Nashville the previous night.
Blues coach Ken Hitchcock got his 600th career win against the franchise he beat for his first victory when the his Dallas Stars won at Vancouver on Jan. 22, 1996.
Security was increased a day after the bombings at the Boston Marathon with all fans getting wanded on their way into the Scottrade Center and bomb-sniffing dogs observed. A moment of silence was observed before the anthems.
The Blues entered the game in seventh place in the Western Conference, one point ahead of Columbus and Detroit with seven to play, including six at home. They were 0 for 4 on the power play, extending a run of futility to 6 for 76.
The Blues had been outscored 7-0 over three games since Kevin Shattenkirk's first-period goal in a 4-1 loss at Columbus on Friday night before Bouwmeester, a key acquisition on defence for the stretch, scored his first goal in eight games with St. Louis to tie it midway through the third.
Bouwmeester got his seventh of the season on a 2-on-1 rush at 10:50, driving the net on Schneider after collecting a puck that went between the legs of a Vancouver defender. The play was set up by a pair of players in deep slumps with David Perron earning just his fourth point with no goals in 16 games and Alex Pietrangelo getting his fourth point in 17 games without a goal.
The Canucks were outshot 25-11 through two periods, but needed just one shot on a power play late in the second to take the lead and end a string of 25 straight penalty kills by St. Louis.
With Vladimir Sobotka off for hooking, Edler threaded a high drive through traffic past Brian Elliott that clanged off the far post. Both Sedins assisted on Edler's seventh goal of the season, giving Henrik Sedin 11 points in his last seven games and Daniel Sedin nine in that same span.
Seconds earlier, Schneider denied Alex Steen on a 3-on-2 short-handed rush.
NOTES: Steen is among several Blues still struggling with one goal in 12 games. Patrik Berglund has one goal in 13 games, an empty-netter, and Chris Stewart has one goal in 12 games after scoring nine goals in eight games. ... The Sedin twins each have four points in three games against the Blues this season.