The Stars will face the Colorado Avalanche, who eliminated the Winnipeg Jets in five games, in the second round.
Radek Faksa and Wyatt Johnston scored, and Jake Oettinger made 21 saves for Dallas, which is the No. 1 seed from the Central Division.
Brett Howden scored, and Adin Hill made 22 saves for Vegas, which was the second wild card from the Western Conference.
Johnston gave Dallas a 1-0 lead at 14:34 of the first period when he intercepted a clearing attempt by Vegas defenseman Shea Theodore and scored from the high slot. The goal came shortly after Jonathan Marchessault hit the post with a wide-open net.
Howden tied it 1-1 at 15:25 of the second period, tapping in a backdoor pass from Michael Amadio at the left post on a rush.
Faksa scored 44 seconds into the third period to put the Stars back in front 2-1. He kicked a pass from Craig Smith to his stick and scored with a backhand from the right circle that deflected off Alec Martinez.
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