Stone has an NHL-best 16 points (six goals, 10 assists) and five multipoint games in March, which have all come during his streak.
"Tonight wasn't a Picasso. We had a soft start," Stone said. "We were able to buckle down and get things in the right direction."
Max Pacioretty had a goal and an assist, and Marc-Andre Fleury made 23 saves in his 16th start in 17 games for the Golden Knights (19-6-1), who have won three straight. They will play the Sharks here again Wednesday.
It was Fleury's 481st NHL win, three behind Ed Belfour for fourth in NHL history.
"I kind of expected the start. It looked like we had been on the road for 10 days," Vegas coach Peter DeBoer said. "I felt at morning skate our energy was off. I felt it was going to take a little while to work into the game. Thankfully, [Fleury] was our best player in the first and allowed us to get our legs under us."
Timo Meier scored, and Devan Dubnyk made 34 saves for the Sharks (11-12-3), who had their three-game winning streak end.
"I thought there were a lot of good things to take from this game," San Jose coach Bob Boughner said. "Fleury was the difference maker. That's a good team over there, but I thought we did good things and fought hard."
Pacioretty scored for the second consecutive game, on the power play, to give the Golden Knights a 1-0 lead at 8:35 of the first period.