Alec Martinez scored twice, William Carrier had a goal and an assist, and Robin Lehner made 31 saves for the Golden Knights (25-10-2), who were 0-2-1 in their previous three games.
"Coming off the last two games, one of the things we didn't like was not putting the puck in the back of the net," Martinez said. "We tried to create opportunities. The forwards did a really good job of getting bodies in front of the goalie. It paid dividends."
Ville Husso allowed five goals on 18 shots for the Blues (16-16-6), who have lost seven straight (0-6-1) and eight in a row at home (0-6-2). Husso was replaced in the second period by Jordan Binnington, who made 12 saves on 13 shots.
The teams will play again here Wednesday.
Vegas defenseman Alex Pietrangelo had an assist in his first game back in St. Louis since he signed an eight-year contract as a free agent Oct. 12. He played his first 12 NHL seasons with the Blues after they selected him with the No. 4 pick in the 2008 NHL Draft.
The Blues played a video tribute for Pietrangelo five minutes into the first period.
"I was just saying to [St. Louis forward Vladimir Tarasenko], it was harder before the game because I think of the emotions," Pietrangelo said. "Once you get in the game, you push that all aside. Once the video passed, and I knew that was coming, which was obviously special. That was a great job. That was important to me with my wife and kids in the stands. Then it was business as usual."