Jeff Tambellini scored a late power-play goal, Mikael Samuelsson had two assists and Roberto Luongo stopped 15 shots to earn his 13th career victory against the Blues in 22 games. Vancouver improved to 9-1-1 in its last 11 games.
"I think we're playing with confidence, but at the same time, we're not satisfied," Kesler said. "It's business as usual around here. We've got to keep going.
"You look at the standings and there's not a lot of space [in the Western Conference], so we've got to keep winning and staying on this W-train."
Alexander Steen scored for the Blues, his third goal in two games this season against the Canucks. St. Louis has one win in its last five games and has scored two goals in two games.
"There wasn't a lot of space or opportunity to be had out there," Blues coach Davis Payne said. "You had to fight for everything you got.
"We beat people with real smart, predictable plays on our own part. That's something we're going to have to address and make sure it shows up in Atlanta [on Tuesday]."
Volpatti took advantage of a Blues turnover in their zone, as Tanner Glass checked defenseman Alex Pietrangelo in the left corner to allow Alexandre Bolduc to center a puck to Volpatti, who beat Jaroslav Halak 7:12 into the second period for the first goal of the game.
"Obviously, I didn't have many goals in the American [Hockey] League so it's nice to come up here and get one and break the goose egg finally," Volpatti said.
Kesler made it 2-0 after the Canucks broke out on a 2-on-1 play, with Kesler keeping the puck and snapping a shot past Halak at 9:16 of the second.
The Blues, who were outshot 20-10 through two periods, finally got an opportunity and Steen cashed in on a backhander from the slot with 2:03 to play in the second to slice Vancouver's lead to 2-1.
"We were just one shot from tying her up," Steen said.
The Canucks, who came in with the third-ranked power play in the NHL, had four opportunities -- including a 35-second stretch of 5-on-3 -- to break a scoreless tie in the first period but were denied by the Blues each time.
But spending nearly half the period on the penalty kill took away any offensive momentum St. Louis was trying to gain.
"It definitely doesn't give us any momentum going the other way," said defenseman Barret Jackman, one of the mainstays on the Blues' penalty-killing unit. "It took a lot of guys out of the game when you're sitting in the box and we're rolling over our penalty killers."
Vancouver outshot St. Louis 12-3 in the opening 20 minutes.
Tambellini scored with 1:37 to play from the slot to give the Canucks a two-goal lead.
Replays showed Bieksa might have been hit by his own stick. But the Blues, who were down a goal, lost a chance to tie it.
"That's the human element of the game," Backes said. "I'm not going to criticize. They're doing the best job they can, but that's our puck in their zone with a couple guys in front and 3:30 left in the game. Tough break there, but there's 55 other minutes of the game that we need to do more."
Blues D Roman Polak (wrist) and Pietrangelo (upper-body) returned to the lineup. Polak missed 24 games with a severed tendon in his right wrist. Pietrangelo was out three games. ... Canucks LW Daniel Sedin has 14 points in 11 games. C Henrik Sedin and Kesler each have 13 points in 11 games. ... The Blues are in the middle of a 15-game stretch with 12 at home. ... The Canucks were without LW Mason Raymond (thumb) and D Sami Salo (ankle). ... Blues RW B.J. Crombeen played his 200th career game. ... St. Louis was held to 16 shots, one off its lowest output of the season. ... Halak stopped 26 shots.