Vegas (11-6-1) held Vancouver to five shots on goal in the third period, when Erik Haula, Jonathan Marchessault and Reilly Smith scored.
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"It's part of my job to come back after a performance where you probably wanted to have two or three goals back," said Lagace, who started the season as the Golden Knights' fourth-string goalie before injuries to Marc-Andre Fleury, Malcolm Subban and Oscar Dansk led to him assuming the starting role. "The guys played awesome in front of me, kept the work pretty limited in the second and third. That's a team win."
Lagace was removed in the third period of the loss to Edmonton with lower-body soreness, but he came back strong Thursday. He stopped Brandon Sutter on a shorthanded breakaway 4:42 into the second period and made a good left-pad stop on a hard Brock Boeser shot with 6:57 left in the third and Vegas leading 3-2.
"I'm smiling every day I'm up here," Lagace said. "To win, it's candy for me."
Haula, who also had an assist, scored the go-ahead goal 6:27 into the third period. James Neal stole the puck from defenseman Erik Gudbranson behind the Vancouver net and fed it out front to David Perron, who made a backhand pass through the crease to Haula.
Haula has four goals and four assists in his past six games but was more focused on bearing down defensively after the loss in Edmonton.
"We had to," Haula said. "You let up eight goals, it's not what you want. You can't pin that on the goalie. Our goalies have been great, whoever's in the net. Give a lot of props to Max."