Roope Hintz scored the only goal in the shootout.
"They've got a good defensive team," Stars coach Peter DeBoer said. "That's arguably the best defense in the League. They're not going to give you a lot. At the same time, I thought we didn't make it tough enough on them most of the night anyway. You get 80 games in, you're not going to complain about wins against good teams. We found a way to get two points, which is the most important thing this time of year."
Brett Howden scored, and Jonathan Quick made 24 saves for the Golden Knights (49-22-9), who are 7-1-3 in their past 11 games and extended their point streak to six games (3-0-3).
Vegas, which is in first in the Pacific Division, two points ahead of the Edmonton Oilers, can finish no lower than second.
"I think all these games lately have had that [playoff] feel to it," Howden said. "Obviously, for us, they're important points. Coming down to the end here, we want to shape our game to be ready for the first game of the playoffs, but also still trying to get some points. I think every game has kind of had that feel lately."
Howden scored on a breakaway to make it 1-0 at 14:21 of the first period on a pass from Keegan Kolesar.
"That was a tight-knit game," Vegas defenseman Ben Hutton said. "It was almost like a playoff-like feel out there. There were some hits, some big blocks. We were doing what we could to win. A bounce here, a bounce there and it could have been a different story, but it was a good game."