Trevor van Riemsdyk and Dylan Strome scored, and Kuemper made 38 saves for the Capitals (31-28-7), who are five points behind the Pittsburgh Penguins for the second wild card into the Stanley Cup Playoffs from the Eastern Conference. Pittsburgh has two games in hand.
"We definitely needed two (points)," Capitals coach Peter Laviolette said. "We had chances I think to score and weren't able to capitalize. They certainly had their chances as well. I though Darcy played an unbelievable game, but you have opportunities, we just couldn't get it done. I think you look back with frustration."
New Jersey outshot Washington 30-11 over the second and third period.
The Capitals took a 1-0 lead with 10 seconds remaining in the first period when van Riemsdyk's shot from above the right face-off circle deflected in off the leg of Devils defenseman John Marino.
"I think we started off maybe a little sluggish, then that second half of the first I thought we were good," van Riemsdyk said. "I thought we had moments where we were very good."
Haula tied it 1-1 during a power play at 6:55 of the second period when his pass attempt deflected in off Washington defenseman Alexander Alexeyev.
"I was looking for my buddy [Ondrej Palat] backdoor, but I got a nice bump," Haula said.
Mercer gave New Jersey a 2-1 lead at 7:32, knocking in the rebound of Nico Hischier's shot.