"Every time you get in there, you get nervous trying to live up to [Fleury's] standards," Subban said. "The boys played well in front of me tonight and made it easy on me."
Berglund beat Subban 2:54 into the game to give the Blues a 1-0 lead.
Karlsson took a stretch pass from Cody Eakin and scored on a breakaway for his third shorthanded goal of the season to tie it 1-1 at 6:18. It was Karlsson's 41st goal, four behind Alex Ovechkin of the Washington Capitals for the NHL lead.
Marchessault gave the Golden Knights a 2-1 lead at 13:31 with his first of the night, but Schenn scored his first goal since March 17 to tie it 2-2 at 16:09.
Vegas took a 3-2 lead at 16:35 of the second period on Neal's 25th goal, his first in 13 games dating to Feb. 8.
"I think sometimes, when you go into slumps coming back from injury, you just want to get your legs under you. When you're not getting chances or the looks, you've got to do something different," Neal said. "I felt the past three games I was getting better looks, better shots. I felt like I was going to get something."
Thorburn scored at 6:14 of the third period to tie it 3-3. It was his first goal in 83 games dating to Dec. 11, 2016.