Vegas forward James Neal nearly scored on a breakaway after coming out of the penalty box in the first period, but Gibson made the save at 13:57.
Karlsson scored 28 seconds into the third period to make it 3-1. After defenseman Josh Manson turned over the puck in the Anaheim zone, Jonathan Marchessault had time to pull up in the left circle and wait to pass to Karlsson, who redirected the puck past Gibson.
Perron scored into an empty net with 1:13 remaining to make it 4-1.
The Golden Knights are 3-0-0 against the Ducks and in first place in the Western Conference.
"They played well," Getzlaf said. "They are where they are in the standings because they play hard. They've bought into the team game they've needed to play."
Rakell scored his Anaheim-leading 11th of the season on the first shot on goal of the game. After Vegas forward Erik Haula blocked defenseman Brandon Montour's slap shot, Jakob Silfverberg got to the puck and passed from behind the net to Rakell, whose one-timer at 1:40 made it 1-0.
Subban, making his second start since Dec. 8, stopped all 27 shots he faced the rest of the way.
"He's a competitor," Eakin said of Subban. "He's an athlete. He's a player."
The Golden Knights tied it 1-1 on a goal by Theodore at 17:50. Oscar Lindberg dug the puck off the right wall in the Ducks zone to Tomas Nosek, who passed to Theodore for a wrist shot past Gibson from the left circle.
"I feel like when I get the puck, I'm thinking shot a little bit more," said Theodore, who played 53 games for the Ducks from 2015-17. "I feel like I'm getting lucky on some of the goals."
Theodore was traded by Anaheim to Vegas at the NHL Expansion Draft on June 21. Perron played 28 games for the Ducks during the 2015-16 season, and Karlsson played 18 games for Anaheim in 2014-15.
The Golden Knights played significantly better in the second and third periods.
"We know what our strengths are, and that break in between (periods), we come in and we talk about it a little bit and we just focus," Theodore said. "I feel like that's definitely a good thing about our team."