"It means a lot to us," Golden Knights defenseman Deryk Engelland said. "This is what you play for all season. After [the Oct. 1 mass shooting in Las Vegas that killed 58 and injured hundreds more] those first games ... you want to play for the city, the people that were affected by it. To make this run, win this series, it's awesome for us, but it all comes back to the city and the people affected by that."

[WATCH: All Golden Knights vs. Jets highlights | Complete Jets vs. Golden Knights series coverage]

Alex Tuch and Ryan Reaves scored, and Marc-Andre Fleury made 31 saves for the Golden Knights, who became the third team to advance to the Cup Final in their inaugural season, joining the Toronto Arenas (1918) and St. Louis Blues (1968). Vegas also became the sixth team to reach the Cup Final in its first postseason appearance, joining the Montreal Maroons (1926), Boston Bruins (1927) and Florida Panthers (1996).

Video: VGK@WPG, Gm5: Tuch opens scoring off turnover

"The whole mentality of this team is next man up," Reaves said. "We've got a deep team, we've got a lot of good players. You look at the season this team had even before I got here, everybody's stepping up. The guys that weren't playing, myself included, we stayed ready. We had fun while we were doing it, but we worked hard so when we were called upon we were ready to go."

Josh Morrissey scored, and Connor Hellebuyck made 30 saves for the Jets, who lost four straight after winning Game 1.

Video: VGK@WPG, Gm5: Morrissey nets slapper off the draw

"I still think we did things right, got our chances," Hellebuyck said. "Luck was on their side, definitely. I've never seen anything like it. Even their goals tonight were two tips. I don't know. It's tough to swallow."

Reaves scored to give the Golden Knights a 2-1 lead at 13:21 of the second period, redirecting Luca Sbisa's shot from the point. The goal was his first with the Golden Knights since being acquired in a trade with the Pittsburgh Penguins on Feb. 23.

Video: #ThirstForTheCup: Vegas advances to Stanley Cup Final

Tuch made it 1-0 at 5:11 of the first period, beating Hellebuyck blocker side from the high slot off a turnover by Morrissey, whose outlet pass hit the skate of Ryan Carpenter and bounced to Tuch.

Vegas is 10-1 in the Stanley Cup Playoffs when scoring first.

Morrissey tied it 1-1 at 17:14, scoring on a one-timer off a face-off win by Bryan Little.

"Throughout this whole thing until that buzzer blew tonight, I never thought we were out of it, never thought we wouldn't find a way back into it," Jets captain Blake Wheeler said. "It just seemed like every time we grabbed some momentum, they took it. So we can use whatever we want to do, but you have to give them a ton of credit for doing that. It's the sign of a good team."

Goal of the game

Reaves' goal at 13:21 of the second period. 

Video: VGK@WPG, Gm5: Reaves tips in point shot for lead

Save of the game

Fleury's save on Wheeler at 16:08 of the third period.

Video: VGK@WPG, Gm5: Fleury denies Wheeler with his pad

Highlight of the game

Fleury's save on Little at 12:11 of the third period.

Video: VGK@WPG, Gm5: Fleury makes pad save on bouncing puck

They said it

"It's insane. If you go back to the beginning of the season, your goal is always to make the playoffs. But if I were to guess I would be sitting here doing this right now, you would be a little skeptical at the time. But once we got rolling, we saw we have a team that can do some damage and a phenomenal goalie that's going to stop everything. It's been an amazing ride. We just want to keep it going now." -- Golden Knights defenseman Deryk Engelland 

"It was their time. They're just playing really well. And you have to give them all the credit. Typically, in a seven-game series, the better team wins. Coming into it, I thought we had the best team. I felt that way and obviously I'm a little bit biased, standing in this room feeling that we had a great opportunity. And that team just ... it was their time. They made it really tough for us. We had to work for everything we got and even when we broke them down, we just couldn't seem to ever gain the type of momentum we needed to get this thing on our terms." -- Jets captain Blake Wheeler

Need to know

Fleury has 74 wins in the playoffs, tying him with Chris Osgood for eighth place in NHL history. … Jets defenseman Dmitry Kulikov returned to the lineup for the first time since March 8 (31 games) because of a back injury and had one shot in 9:28. … Vegas is the seventh team in NHL history to win three series on the road to reach the Cup Final (five of the previous six won the Stanley Cup).

What's next

Golden Knights: Game 1 of Stanley Cup Final, TBD

Jets: Season over

Video: Golden Knights win Game 5 to advance to Cup Final