The Wild, the No. 3 seed, played Game 7 for the third time in their history after trailing a best-of-7 series 3-1. Kirill Kaprizov and Zach Parise scored, and Cam Talbot made 29 saves.
"I think we all firmly believed with where we were a handful days ago, down 3-1 and making it 3-3, we all firmly believed we were going to win this game tonight," Parise said. "We didn't quit. We played, we competed, but just couldn't get that third one."
It's the third consecutive season the Golden Knights played Game 7 after leading a series 3-1; they defeated the Vancouver Canucks in the second round last season and lost to the San Jose Sharks in the 2019 first round.
"You hope that moments like that galvanize your group," Vegas coach Peter DeBoer said. "When we talked this morning in our team meeting, we talked about how we felt we were prepared for this tonight. We were ready to go and we had all hands on deck … we felt with that lineup that we would be a hard team to beat tonight."
Janmark gave the Golden Knights a 1-0 lead at 5:09 of the first period after getting a loose puck and deking to his forehand. Parise tied it 1-1 at 16:49 when he deflected Ryan Suter's shot between his legs.
Nicolas Hague gave Vegas a 2-1 lead 2:05 into the second period with a shot from the point off a face-off from the left circle.
"It was a ton of fun," Hague said. "The building was rocking, which is always awesome, but it was on another level tonight. A little nervous at first, but boy was it fun."