Subban made 42 saves in his first start since Feb. 2. He played in place of Marc-Andre Fleury, who missed the game with an undisclosed injury.
"They put a lot of traffic in front and you have to track the puck as best you can," Subban said. "There were times I couldn't see it, but guys made huge blocks when I couldn't see the puck."
Tomas Tatar scored for the Golden Knights, who lost for the first time in three games.
The Golden Knights became the first team in NHL history to reach 100 points in its inaugural season.
"It's a huge point," Vegas coach Gerard Gallant said. "I thought we played an excellent first period, and San Jose took over a little bit in the second period. Both teams played an OK game, but I think you'll see better from both teams."
Tatar scored at 3:47 of the first period to give Vegas a 1-0 lead. Tatar cut in front of the crease, took a pass from Marchessault, and beat Jones with a backhand.
Subban made a save on all 13 shots he faced in the first, and Jones made 10 saves.
The Sharks outshot the Golden Knights 18-4 in the second period and tied it 1-1 at 3:27 when Burns scored with a wrist shot through traffic from the point for his first goal since Feb. 15.
San Jose went 0-for-6 on the power play. Vegas 0-for-2.
"It's a team that's ahead of us in the standings," Sharks coach Peter DeBoer said. "It's a good measuring stick for us for where we're at as the season winds down. We knew it was a big game. I thought we started a little bit tentative the first 10 minutes. I didn't feel we were playing our game, but I thought as the second half of the first period came around, we started to play, and then in the second and third I thought we really found another level."
