Mitch Marner scored an empty-net goal at 19:54 for the 3-1 final.
Game 2 of the best-of-7 series will be here on Wednesday (9:30 p.m. ET; HBO MAX, truTV, TNT, SN360, SN, TVAS).
“It’s Game 1. It is (about) which team finds its game the quickest that has the advantage,” Golden Knights coach John Tortorella said. “We’re fortunate. Fortunate that we found a way to win. They played well. Some of it had to do with them. They played well, but we have some things to work on.”
Brett Howden scored for the fourth straight game, and Carter Hart made 33 saves for the Golden Knights, who are the No. 1 seed from the Pacific Division.
Mikael Granlund scored, and Lukas Dostal made 19 saves for the Ducks, who are the No. 3 seed from the Pacific.
“I don’t mind the way we played,” Anaheim coach Joel Quenneville said. “We had a lot of pace. Both teams worked hard. It’s a heck of a hockey game. ... I don’t think we had the quantity or the quality we had in the last series, but we did have enough to score more than one."
Howden put Vegas ahead 1-0 at 3:14 of the second period. Marner sent a backdoor pass to a driving Howden, who tapped the puck into an open net at the left post.
“I was just looking at Mitch right away,” Howden said. “He made a great play. I was kind of behind the play, and I could feel that he knew I was coming late. I was going to get there a bit earlier, and he waited it out, and I just tried driving back away.”