Jonathan Marchessault had a goal and an assist for the Golden Knights (46-21-6), who have won four straight and eight of their past nine. Brossoit made 27 saves in his first start since Feb. 25 because of a lower-body injury.
Vegas remained four points ahead of the Los Angeles Kings, who have one game in hand, for first place in the Pacific Division.
"It's a big win, a big (three-game) road trip," Golden Knights defenseman Brayden McNabb said. "[The Oilers] were sneaking up on us (in the standings), and we were able to get an extra point out of this game. We have that next-man up mentality, it's been that way all year. We've had injuries throughout the year, the guys are prepared, we have great depth, we have great goaltending, and it showed tonight."
Leon Draisaitl had a goal and an assist, and Stuart Skinner made 30 saves for the Oilers (41-23-9), who had their five-game winning streak end.
Edmonton is seven points behind the Golden Knights and three ahead of the Seattle Kraken, who hold the first wild card into the Stanley Cup Playoff from the Western Conference.
"It was a tight game. It was what you expect in the playoffs," Draisaitl said. "It is obviously a team that we could face. I think we know how to handle these types of games. Tonight didn't go our way, but we will take the point."