Marchessault's goal came after Vegas goalie Logan Thompson made a glove save on Pavel Buchnevich on a penalty shot 30 seconds into overtime.
"Certainly he's a player you want [to have] that opportunity. The goalie made a good save," St. Louis coach Drew Bannister said of Buchnevich. "That's part of the game."
Said Vegas forward William Karlsson: "I think the word is clutch that we're looking for. They were clutch, and obviously a huge save there on that penalty shot in OT. That's what we need from the goalies at this time of year."
Pavel Dorofeyev scored for the Golden Knights (39-25-7), who have won six of eight and moved five points ahead of the Blues for the second wild card into Stanley Cup Playoffs from the Western Conference. Thompson made 31 saves.
"Just where we are right now matters," Cassidy said. "If it's earlier in the regular season, you don't worry so much about it. ... You want to make sure you walk out of here with the extra point. I thought it was a real well goaltended game, to be honest, at the end of the day. Both goalies gave their teams great chances to win, and we were one shot better."
Brandon Saad scored, and Binnington made 32 saves for the Blues (38-30-4), who are 6-1-1 in their past eight games.