Braden Holtby made 26 saves for the Capitals (22-13-2), who were coming off a 3-2 overtime loss at the Arizona Coyotes on Friday. It was Holtby's third loss in 12 starts.
"We knew it was going to be hard back-to-back," said Capitals captain Alex Ovechkin, who had three shots on goal. "I think if it was not for [Holtby], it would be like 10-0 after the first period. That's why he's one of the best goalies in the League."
The Golden Knights scored three goals in the opening 14:55.
"We lost it really in the first 10 (minutes)," Capitals coach Barry Trotz said. "We talked about this team, how they like to jump on teams. They got a team that competes hard on pucks. We said if you're not ready for the speed and pressure, they'll just overtake you."
Cody Eakin got his 100th NHL assist when he helped set up Tuch's goal at 2:37 for a 1-0 lead.
Lindberg scored at 7:39 to make it 2-0. Tomas Nosek led a 4-on-2 rush for the Golden Knights and passed the puck to Lindberg, who beat Holtby top shelf from the top of the left hash marks.
Karlsson scored his first goal since Dec. 8 at 14:55 to give the Golden Knights a 3-0 lead. Jonathan Marchessault, whose 32 points lead Vegas, earned his 20th assist.
The Golden Knights are 15-2-1 at home after going 4-0-1 on their five-game homestand.
"This is definitely the best home crowd I've ever played in front of," Tuch said. "The momentum the fans give us is unbelievable."