Robin Lehner made 35 saves, including 16 in the first period, and William Karlsson scored for the Golden Knights (1-2-0).
"He was our best player tonight," Karlsson said of Lehner. "He gave us a chance to win the game."
Lehner allowed four goals through two periods Thursday, a 6-2 loss at the Los Angeles Kings. He said his teammates' work ethic and the mentality to shoot was much better after a five-day break.
"We just needed to create a bit more chaos, I think," Lehner said. "But we've got to clean up some ... I don't know how many breakaways or 2-on-1s (we allowed). That's not been [a problem] since I've been here. If we clean that up, we can give ourselves a better chance."
Vegas played its first game without forwards and leading scorers Max Pacioretty and Mark Stone. Pacioretty is week-to-week with a lower-body fracture; Stone, the Golden Knights captain, has a lower-body injury.
"This is a league where it's the first team to three usually," Vegas coach Peter DeBoer said. "We've got to find three goals a night, someway somehow. I know [Karlsson's] line consistently is going to chip one in for us. Where are we going to find the other two?"
Karlsson scored at 8:17 of the first period to give the Golden Knights a 1-0 lead. He finished a 2-on-1 with Reilly Smith and scored on a rebound after Binnington made a save on the initial shot.
Vegas was outshot 7-2 in the first eight minutes but outshot St. Louis 17-16 after the first.