Cody Eakin, James Neal and William Karlsson scored, and Marc-Andre Fleury made 37 saves for the Golden Knights.
Anze Kopitar had a goal and an assist, Alex Iafallo scored his first NHL playoff goal, and Jonathan Quick made 23 saves for the Kings, who trail 3-0 in a series for the ninth time.
Neal beat Quick five-hole at 14:23 of the third to give Vegas a 2-1 lead, and Karlsson made it 3-1 at 14:44 with a one-timer off Reilly Smith's backhand pass from near the end boards.
"I think when you do the right things, if you're finishing your checks, you're playing well defensively, the goals will come," said Neal, who scored his 26th NHL playoff goal. "I've been in enough of those games, I feel like if you stick with it, you'll get your chance."
Kopitar tipped Oscar Fantenberg's shot past Fleury to pull the Kings within 3-2 with 2:04 remaining.
The Golden Knights tied it 1-1 at 6:10 when Eakin scored with a one-timer from the right face-off circle off a pass from Ryan Carpenter after Colin Miller hit the crossbar earlier in the sequence.
Los Angeles coach John Stevens pointed out that all three Vegas goals came on plays off the wall.
"First goal came from a stalled puck off the forecheck where we got beat on the wall. Second goal came from a play we got beat off the wall," Stevens said. "It's unfortunate. I thought we made a good push here tonight, created a lot more zone time, and made Fleury work a little harder than he had to this point in the series, but had some critical errors at critical times along the wall ended up costing us."
The Kings took a 1-0 lead at 13:14 of the first period, their first lead in the series. Iafallo shot into the top of the net from close range, but play continued for three seconds. After a stoppage, the Situation Room reviewed the play and ruled the puck crossed the goal line for Iafallo's first NHL playoff point.
Iafallo, who was a healthy scratch for Game 2, had not scored in 12 games dating to March 3.
The Kings outhit the Golden Knights 10-2 in the opening 4:40 and 28-13 in the first period.
"We knew they were going to come out and bring everything they had in that first period, and they definitely did," Gallant said. "They probably should have been up more than one goal."
Vegas is the third NHL team to win at least its first three playoff games, joining the Pittsburgh Penguins in 1970 and the Florida Panthers in 1996. The Penguins (four wins) and Panthers each did so in their third season in the League.
