Vladimir Tarasenko had a goal and two assists for St. Louis (16-16-2). Jordan Binnington made 28 saves.
"It's tough, but guys battled hard. We scored enough goals to win," Blues coach Craig Berube said. "We need more guys contributing, but we got that one line (Tarsesnko, Robert Thomas, Pavel Buchnevich) scoring for us. … It was a hard-fought game. They're tight games. They're exciting games. I liked our effort, but at the same time, we have to clean up some puck play and we got to be a little bit better defensively in our own zone."
Alex Pietrangelo scored on a backhand at at 5:22 of the first period after receiving a Stephenson drop pass to give Vegas a 1-0 lead.
Buchnevich tied it 1-1, scoring from the slot 39 seconds into the second period.
The Golden Knights reclaimed the lead 2-1 when Stone scored off a rebound at 4:29, but Tarasenko tied it 2-2 with a power-play goal from just outside the left circle at 6:17.
Justin Faulk gave the Blues a 3-2 lead with a shot from the right face-off dot at 8:17, but Amadio tied it 3-3 at 18:34 after a cross-ice pass from Stone.
"I didn't think he saw me at first," Amadio said. "It was a great play by 'Stevey' and [Stone]."