"It's special ... it's my first time being in the playoffs," Demko said. "It's a unique circumstance (with goalie Jacob Markstrom being unfit to play), but playoffs nonetheless, and this is what I've wanted to be a part of since I was a kid, so being able to get this opportunity is super special. I want to just keep helping any way I can."
Brock Boeser and Elias Pettersson scored, and J.T. Miller had two assists for the Canucks, the No. 5 seed in the West.
Shea Theodore scored, and Robin Lehner made 15 saves for the Golden Knights, the No. 1 seed.
"We just have to take a look at some video," Theodore said. "There were some mistakes that ended up in the back of our net, and those can't happen this time of year. We just kind of have to refocus and get ready for the next one."
Game 6 of the best-of-7 series is in Edmonton, the West hub city, on Thursday (9:45 p.m. ET; NBCSN, CBC, SN, TVAS).
WATCH: [All Canucks vs. Golden Knights Game 5 highlights]
Pettersson, who was the center on a line with Miller and Boeser in the third period, gave the Canucks a 2-1 lead on a deflection in front of Lehner at 3:19 of the third period.
Pettersson has 18 points (seven goals, 11 assists) in his past 14 games.
"We're been playing with each other all season, we have good chemistry, and I think it was good that we switched up the lines because the first two periods weren't good from our side," Pettersson said. "The coach made some changes, and it worked out."
Demko, a rookie, is the 15th goalie in NHL history, and second in two nights, to make his first NHL playoff start and win when his team was facing elimination. Michael Hutchinson did the same for the Colorado Avalanche in Game 5 against the Dallas Stars on Monday.
"I think at this point you rely on the work you put in," Demko said. "I've been doing my thing in practice, making sure my details were where they needed to be. It's different than a game, but everything you see in a game, you've seen at some point in practice, and you just have to rely on that."
Markstrom (8-6-0) started the first 14 postseason games for Vancouver. As part of the NHL Return to Play Plan, a team is not permitted to disclose player injury or illness information.
Canucks coach Travis Green did not have an update on Markstrom's availability for Game 6.
"We'll see where he's at tomorrow," he said.
Lehner was back in net for Vegas after Marc-Andre Fleury made 28 saves in a 5-3 win in Game 4 on Sunday, the second of a back-to-back.
"[Demko] had a good game," Lehner said. "I thought Vancouver played a little bit better defensively to limit our odd-man rushes against them. I think they played five guys pretty tight and kept us to the outside. We had our moments where we really pushed and got some good opportunities, and [Demko] was there to save them. We just have to go to the next game, and we'll be fine."