Wyatt Johnston also scored, Jamie Benn had two assists, and Jake Oettinger made 41 saves for Dallas (31-17-12), which was 0-3-2 during the skid.
"Just a good hockey game. [Oettinger] kept us in it early in the game in the first period," Stars coach Peter DeBoer said. "They came out quick. We were a little slow out of the gate. It was a hard-fought good hockey game. I'm glad we got out on the right side. We've been on the wrong side too many times. We worked hard tonight. We deserved it."
Laurent Brossoit made 41 saves for Vegas (35-18-6), which is 6-0-2 since the All-Star break.
Brossoit is 1-0-2 in three starts since being recalled from Henderson of the American Hockey League.
"It's three good ones. Should be three wins for [Brossoit]. Unfortunately, he only got the one," Golden Knights coach Bruce Cassidy said. "All the games have gone into extra time. He's done his job very well for us. I'm happy for him. He's a hard-working guy who's worked to get back to this point now this year. It's too bad we couldn't put him in the win column every night. Big picture he's given us solid goaltending."