Andre Burakovsky scored for a third straight game for the Capitals, who have outscored opponents 26-13 during the winning streak.
The Devils (25-34-9) have lost five straight games and have scored two goals or fewer in six of their past seven. Mackenzie Blackwood made 33 saves.
"I thought we had some Grade A chances," New Jersey coach John Hynes said. "Unfortunately, the puck didn't go in for us, but you can't fault the effort, and I think the concepts and things we're trying to work on to get into the scoring area, they're there, we're there. We've just got to find a way to put it in."
The Capitals took a 1-0 lead when Burakovsky scored off a pass from Michal Kempny on a 3-on-2 at 2:40 of the first period. It was his 11th goal of the season.
"For him personally and for us a team, I think it's great that he's started scoring," Capitals forward Nicklas Backstrom said. "He's got a terrific shot, I think. It's good to see him get his confidence back."
Holtby made 10 saves in the first period.
"I was just trying to be into it right from the start," Holtby said. "I know playing a team like them with a ton of injuries, you don't really know. It's hard. Sometimes you come out a little flat."
Backstrom made it 2-0 with a power-play goal at 4:35 of the third period when he tapped in a pass from John Carlson.
Lars Eller scored a shorthanded empty-net goal with 59 seconds remaining for the 3-0 final.
The Devils were 0-for-6 on the power play and are 0-for-24 in their past nine games.
"I just think our decisions on the power play tonight were slow," Hynes said. "We wanted to dust the puck off. We did have some good looks, but I thought the decision-making and the execution wasn't where it needs to be."
