Jordan Binnington made 46 saves for St. Louis, which has lost three games in a row (0-1-2) and leads the Colorado Avalanche by two points for first place in the Central Division.
Stone had four assists, and Max Pacioretty had two goals and an assist for the Golden Knights (29-22-8), who won for the first time in three games (1-1-1). Malcolm Subban made 19 saves in his first start since Jan. 31.
Vegas, which ended a four-game losing streak at home (0-3-1) in the first of a five-game homestand, is tied with the Edmonton Oilers for second place in the Pacific Division, three points behind the first-place Vancouver Canucks.
"I think as a team, we're trying to be successful at home," Marchessault said. "We're not necessarily getting the results we wanted. Right now, we have a nice homestand, and it's time to make a statement here."
Pacioretty and Sanford each scored two goals in the first period.
Sanford gave the Blues a 1-0 lead 25 seconds into the game, and Pacioretty tied it 1-1 on the power play at 1:59.
Pacioretty scored again at 6:34 to give the Golden Knights a 2-1 lead, but Sanford tied it 2-2 at 9:41.