The Blues scored three unanswered in a 2:15 span to regain the lead in the first.
Ryan O'Reilly scored his first goal in 10 games, and first since returning from COVID-19 protocol on Nov. 7, from a sharp angle at 10:15 to cut it to 2-1.
Bozak tied it 2-2 at 11:57 on a rebound of Klim Kostin's redirection in the slot, and Faulk scored his 100th NHL goal at 12:30 on a breakaway after he stripped Nicolas Roy of the puck in his own zone to give the Blues a 3-2 lead.
"That's how we play a system," Faulk said of his goal. "When guys do what they did there, I had to poke it away and get the puck. I wasn't expecting a breakaway by any means. I looked to my left and just saw a blue jersey and realized I had some space. So I was able to go out there and have some fun, I guess."
Brandon Saad scored a power-play goal at 1:28 of the second on a loose puck in the slot to extend the lead to 4-2. He has four goals during a three-game point streak.
"He's played well," Berube said of Saad. "Like I said, he's got great speed, outside speed, and he's heavy. He's heavy on the puck. That's two goals in a row, two power-play goals in a row where he's just battling at the front of the net and gets them."
Niko Mikkola made it 5-2 at 9:37 of the third on a wrist shot from the left circle.
NOTES: Golden Knights defenseman Shea Theodore was minus-2 in 22:35 of ice time after missing two games with a head injury. ... Vegas forward Max Pacioretty missed his 17th game with a foot injury but could return Wednesday at the Nashville Predators. ... Pietrangelo had an assist, his fifth in seven games against the Blues, who he played for in his first 12 NHL seasons. ... Faulk became the first defenseman from the 2010 NHL Draft to reach 100 goals. ... O'Reilly has 17 points (eight goals, nine assists) in 18 games against Vegas. ... Tarasenko has 12 points (four goals, eight assists) in 13 games against Vegas. ... Perron hasn't scored in 13 straight games, but he has five assists in the past three games. ... Mikkola had three hits and was plus-1 in 16:38 in his first game since returning from COVID-19 protocol Nov. 16.