Stephenson scored on the power play to put Vegas ahead 4-3 at 1:38 of the third period. It was the forward's first two-goal game since Jan. 31, 2018, for the Washington Capitals.
Stephenson, coming down the left side, tried to center the puck to Alex Tuch, but it deflected off defenseman Kale Clague's stick and beat goalie Cal Petersen five-hole.
"Pretty lucky goal, but I'll take it," Stephenson said.
Zach Whitecloud scored his first NHL regular-season goal, and Robin Lehner made 29 saves for the Golden Knights (7-1-1), who defeated the Kings 5-2 on Friday. It was Lehner's first win in three starts.
"Beating any team in this league twice is going to be tough," Vegas coach Peter DeBoer said. "You see that when you look around the League. There's no doubt we made it tougher on ourselves tonight. You've got to win all kinds of different ways this season. The bottom line is we're winning in a league that's hard to do so."
Jaret Anderson-Dolan scored his first NHL goal for Los Angeles (3-6-2), which lost its fourth consecutive game despite scoring on its first two shots on goal. Petersen made 29 saves after playing 38:56 in relief of Jonathan Quick on Friday.
"I thought we did a much better job than in games prior," Kings coach Todd McLellan said. "I thought we created a lot of good looks, kept plays alive in the offensive zone. Offensively, I thought we improved as a team tonight."
Anze Kopitar scored 36 seconds into the game to give the Kings a 1-0 lead.