The Sharks had allowed at least four goals in four of their past five games, including a 5-3 loss to the Toronto Maple Leafs on Thursday.
"I think the guys responded," Sharks coach Peter DeBoer said. "We have a smart group. I think they know. There wasn't a lot of messaging, it was just the facts of we were playing a little Russian roulette lately and losing."
Chad Johnson, who had a shutout against the Sharks in St. Louis, made 25 saves for the Blues (7-8-3), who were coming off a 4-1 road win against the Vegas Golden Knights on Friday and playing for the third time in four days.
"It just seems like we take a step back a little bit, maybe get a little too high off last night's win," Johnson said. "It was a pretty emotional win last night and we had to come back and have that same sort of intensity, and I don't know if it was there or not."
The Sharks scored three goals in 4:11 during the second period to build a 3-0 lead.
Karlsson scored a power-play goal from the high slot at 1:42 when he beat Johnson with a slap shot to the upper left corner. Karlsson, who was acquired from the Ottawa Senators on Sept. 13, hadn't scored since March 27 of last season against the New York Islanders, a span of 23 games. He had 10 assists in his first 20 games with the Sharks.
"I've been feeling good all year; it just hasn't worked out on the score sheet," Karlsson said. "But sometimes that's the way it is. I don't think I'm doing anything different now."
Pavelski made it 2-0 at 6:31 from close range after Johnson made a save against forward Timo Meier. Kane extended San Jose's lead to 3-0 at 7:45 with a wrist shot.
Pavelski made it 4-0 at 11:59 of the third period when he took a pass from Couture and roofed a shot over Johnson for his 13th goal of the season.
The Blues outshot the Sharks 11-2 in the third.
"I think the one good thing was that we did show some push in the third period," Blues coach Mike Yeo said. "We obviously didn't grab a goal, but we had some good opportunities and if we could've got one or two, then who knows? But you can't come into a building like this against a team like this and put yourself in a hole like that."