Pavel Dorofeyev scored twice for Vegas and Carter Hart (20 saves) allowed four goals for the fifth consecutive game, the last two resulting in losses.
"We'll be back here," Vegas coach John Tortorella said. "We're just going to do it in a different order."
It's the first time the Golden Knights have lost consecutive games since Games 2 and 3 of the Western Conference First Round against the Utah Mammoth.
"I'm going to leave my clothes here, that's for sure," Tortorella later said. "They'll be in the hotel."
Vegas center William Karlsson left with what appeared to be an injury to his left arm stemming from a hit he took from Carolina defenseman Sean Walker at 8:19 of the second period. Karlsson went to the locker room during a stoppage at 8:35.
Tortorella said he didn't have an update, but he intimated that Karlsson, a center who plays in all situations for the Golden Knights, would not be available for Game 6 at least, saying "he's not going to be with us, probably."
"It's tough," Vegas center Jack Eichel said. "You lose somebody like 'Karl', who's so valuable to our team, has been playing so well -- just means everybody else has to step up. He's a world-class player, he plays in all situations, he's extremely reliable in our own zone, and he creates a lot of offense. So, yeah, I mean, he's a huge part of our group."
Staal joined Yvan Cournoyer (1973, Montreal Canadiens), Jean Beliveau (1956, Canadiens), Maurice Richard (1951, Canadiens) and Cyclone Taylor (1918, Vancouver Millionaires) as the only players to score in five consecutive games in the Stanley Cup Final.
No one has ever scored in six straight games.
"Good company," Staal said, "but I'm looking for wins."