Forward Mark Jankowski contributed a spectacular goal during the third-period surge.
"The two best teams are going at it right now, so obviously it's not going to be a cakewalk," Jankowski said.
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"We have all the belief in our group."
Center Logan Stankoven also scored in the third period to start the comeback.
"It's about not breaking. It's fine to bend a bit, but you can't break," Stankoven said.
Golden Knights star center Jack Eichel remained confident after the overtime defeat.
"We've continued to get better at it as the playoffs have went on, managing momentum swings," Eichel said.
"There are going to be spurts of hockey where things are going really good, and spurts where you've got to manage things."
Andersen's Emotional Journey
Hurricanes goaltender Frederik Andersen has been a key factor in the playoffs, battling through the recent death of his longtime friend and agent, Claude Lemieux.
Following a Game Five victory in the Eastern Conference Final, Brind'Amour praised Andersen's emotional resilience after making 23 saves.
"We weren't sure if he was going to be able to play," Brind'Amour said. "But obviously he shook it off and battled through it."
During the post-game locker room celebration, Hurricanes players awarded Andersen "The Rope" trophy.
"I just can't thank you guys enough for the way you guys supported me the last two days," Andersen said.
"Let's get four more."
Andersen recalled the final motivating words from his late agent: "Just go get it."
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Game Three of the best-of-seven series is scheduled next as the venue transitions to Las Vegas.
