Jamie Benn, Jason Robertson and Mason Marchment scored for the Stars, who are the No. 1 seed from the Central Division. Jake Oettinger made 11 saves.
Game 2 of the best-of-7 series will be in Dallas on Wednesday.
“We didn't give them much, you know?” Dallas coach Pete DeBoer said. “A tight-checking game. I mean, you get to two teams that have played pretty tight. So, that's what it's going to look like, I think. You can't chase the game the whole series. I thought tonight we were chasing the game all night. So, we've got to make sure we fix that going forward.”
Stone put the Golden Knights up 1-0 at 1:23 of the first period when he redirected a shot from Hanifin on the power play.
“That was a big goal for us,” Stone said. “You got to get off to a good start on the road. That’s key.”
Marchessault extended it to 2-0 at 8:27, scoring five-hole on Oettinger.
Benn cut it to 2-1 at 16:07 on a breakaway after receiving a stretch pass from Wyatt Johnston.
Hertl pushed it to 3-1 at 17:51, tapping the puck into an open net off the rebound of Hanifin’s shot.
“Tomas is very good in there,” Cassidy said. “He’s a big man. So, once he establishes a position, he’s going to be hard to move. He’s got quick hands. He showed that. We’ve talked about that since he’s come to our team. We’ve talked about how he’s a natural, true net presence. He showed that tonight.”