Brent Burns, Evander Kane, Tomas Hertl and Marc-Edouard Vlasic each had a goal and an assist, and Erik Karlsson had two assists for San Jose in a rematch of the 2018 Western Conference Second Round, which Vegas won in six games.
Game 2 of the best-of-7 series is Friday at San Jose.
"I thought we played a poised game," Burns said. "We're going to have to play together, stay close to each other with lots of talk. They come hard, they play real physical, and I thought we played a poised game."
WATCH: [Golden Knights vs. Sharks Game 1 highlights | Complete series coverage]
The Golden Knights, who reached the Stanley Cup Final last season as an expansion team, lost a series opener for just the second time. They lost 4-2 to the Winnipeg Jets in Game 1 of the 2018 conference final.
Mark Stone scored twice, and Marc-Andre Fleury made 28 saves for Vegas.
"Definitely not the way we want to start a series," Fleury said. "I think we expected it was going to be intense and physical."
Joe Pavelski was credited with a power-play goal at 14:42 of the first period to give the Sharks a 1-0 lead after Burns' shot deflected off Pavelski's face.
Pavelski did not play the remainder of the first period but returned at the beginning of the second.
"He goes to where it hurts," Sharks forward Timo Meier said. "He's a tough guy and we know that. He shakes off those kinds of things, and he's a leader. He definitely helped a lot in us winning the game tonight."