Brett Connolly scored his 20th goal of the season, and Pheonix Copley made 20 saves for the Capitals (43-23-7), who moved two points ahead of the New York Islanders with nine games remaining. The Islanders lost to the Boston Bruins 5-0 on Tuesday.
"We're in this position and we have to take care of business," Capitals center Nicklas Backstrom said. "You can't rely on other teams. We just have to try to win and go from there. So this is a good win for us."
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Mackenzie Blackwood made 18 saves for the Devils (27-38-9), who are 2-8-1 in their past 11 games.
"They had 22 shots on goal but they had a lot of zone time, so you have to follow the play and be with it every step of the way," Blackwood said. "They could get no shots for 10 minutes, but you still have to do all that work and it could wear you down a bit."
Washington scored the first of three straight in the second period when Connolly got a tip-in at the right post at 5:57 for a 2-1 lead. It is the first time he scored 20 goals in nine NHL seasons.
"He's had a really strong season," Capitals coach Todd Reirden said. "Consistent, confident, playing his best hockey. It was just a matter of time before he was going to get 20. He's put himself in good spots to create, has an offensive mind, thinks offensively. He's got a good shot and a quick release. That is going to be key for us moving forward, to have scoring depth throughout our lineup."
Evgeny Kuznetsov scored at 12:16 for a 3-1 lead, and Tom Wilson scored from the left circle off a pass from Alex Ovechkin to make it 4-1 at 13:28.