Michael Amadio scored for the Golden Knights (25-15-2), who have won their past two games after losing three in a row (0-1-2). It was their first road game since Dec. 28 and the start of a four-game trip that includes games at the Carolina Hurricanes, Florida Panthers and Tampa Bay Lightning.
"It's nice when I get a shutout, for sure, but it's just nice to start the road trip with a win," Lehner said. "Big road trip and it was two big points for us."
Vitek Vanecek made 28 saves for the Capitals (23-11-9), who were 0-for-5 on the power play and shut out for the first time this season. They have lost seven of their past 10 games (3-5-2).
"Everybody hates losing," Washington coach Peter Laviolette said. "Nobody likes the scoreboard and the way it looks right now, so that's what's lousy about it. But I think if the guys continue to work and do the right things, eventually they'll get rewarded."
Amadio gave Vegas a 1-0 lead at 5:29 of the second period when he swept in a rebound after Vanecek saved Brett Howden's shot from the left point.
"I just found myself in front of the net trying to battle and I snuck behind their defenders and just tapped it in there," Amadio said.