Karl Alzner and Brooks Laich also scored to help Washington win its second straight and third in the last five to improve to 12-10-4.
"It's discovering the identity and finding how we're going to have continuous success. You saw it tonight," Laich said. "It was a pretty disciplined, structured game.
"The compete level, the attention to detail, the work ethic has to be in the game every day for us to have success."
Patrik Elias scored and Cory Schneider had 25 saves while starting for the 25th time in New Jersey's 27 games this season. The Devils have lost eight of their last 10 and are 3-5-1 against Metropolitan Division teams.
"We want to find our identity at home," Adam Henrique said. "We have to find a way to string some wins together."
New Jersey dropped to 3-4-3 at Prudential Center, having played the fewest home games of any NHL team this season.
"If we don't have a great home record we're not getting into the playoffs," Devils coach Pete DeBoer said.
Washington took control with the two goals in the second period to take a 3-1 lead.
Beagle gave the Capitals the lead with his fourth of the season with 9:15 remaining in the period with a backhander past Schneider. Kuznetsov increased the advantage with a power-play goal from the right circle at with 7:20 left.
"We just wanted to stay on the gas, honestly," Laich said of the second period in which the Capitals outshot New Jersey 13-8. "The first period, we thought we had a good period. We really felt we had our legs under us and found our game. We just wanted to stay with it."
Laich's empty-netter with 23 seconds remaining capped the scoring.
Washington finished 1 for 2 on the man advantage, while killing both of New Jersey's chances. The Devils had entered the game tied for 10th in the NHL in power-play success rate.
During New Jersey's second power play, many of the announced 15,230 in attendance booed the man-advantage units before sarcastically cheering the Devils when they entered the Washington zone.
"Obviously, you never want to hear that," Henrique said. "We were frustrated, too."
The Metropolitan Division rivals traded early goals, as Alzner opened the scoring at 3:47 of the first period. He ripped a shot from the left wing circle past Schneider for his first of the season after Andy Greene was unable clear the puck from the defensive zone.
Elias tied it 3:03 later when he knocked Dainius Zubrus' shot over Holtby for his third of the season, and the 396th of his career. Elias, a career-long Devils player, is also five points away from 1,000.
The Devils finished with an 34-29 advantage in shots on goal.
"They're a team that really gets to the front of the net and use their `D' a lot," Capitals coach Barry Trotz said. "But for the most part we did a pretty good job and (Holtby) did a really good job for us as well."
NOTES: New Jersey announced RW Damien Brunner cleared waivers. Signed to a two-year, $5 million contract last September, Brunner recorded 32 points in 77 games spanning the 2013-14 and 2014-15 seasons. "It wasn't working," DeBoer told reporters after the morning skate at AmeriHealth Pavilion. It is unclear if Brunner will report to New Jersey's AHL affiliate in Albany, N.Y. ... Both the Capitals and the Devils held their morning skates at AmeriHealth Pavilion instead of the Prudential Center because Seton Hall and Rutgers had the Prudential Center for a men's college basketball game at noon. ... The Capitals scratched LW Andre Burakovsky and center Liam O'Brien. ... New Jersey scratched D Adam Larsson and C Jacob Josefson.