The Devils finished with 112 points, one point behind the Carolina Hurricanes, who defeated the Florida Panthers 6-4. New Jersey will have home-ice advantage against the third-place New York Rangers in the first round of the Stanley Cup Playoffs.
"We talked about step one. That was step one, to make sure that we're in the playoffs, play good hockey," Devils coach Lindy Ruff said. "And now the stage gets bigger. The opportunity to accomplish and keep moving on will be in front of us and you've got to just really wrap your arms around this moment."
Erik Haula scored two goals for the Devils (52-22-8), who set a franchise wins record by rallying from down 4-1 in the third period. Mackenzie Blackwood was lifted early in the second period after allowing four goals on 11 shots. Akira Schmid made 20 saves in relief.
"It's a great accomplishment," Haula said of the wins record. "What a way to end the year and just the overall journey of 82 games, how we got better, how we matured, how we learned a lot along the way. And now we put ourselves in a great spot and we're excited for an opportunity to go on a run."
Craig Smith scored his 200th NHL goal for the Capitals (35-37-10), who will miss the playoffs for the first time since 2013-14 after going 2-8-3 in their final 13 games. Darcy Kuemper made 29 saves.
Washington captain Alex Ovechkin played 20:02 and had an assist in his return after missing three games with an upper-body injury.
"Season's done, nothing you can do," Ovechkin said. "I'm always saying during the year, 'Every point is an important point,' right? You have to collect as many as possible at the beginning so you're not in this situation like we were two months ago. We have to chase the team, and if we get two points, teams ahead of us get another two points. If we lose, they win, so it's kind of up and down for us."
Haula scored on a breakaway at 3:17 of the third period to pull the Devils within 4-3, and Dougie Hamilton tied it 4-4 at 12:23, scoring on a one-timer from the center point off a pass from Damon Severson.
"I think they probably started cheating for offense a little bit and we just didn't do a good job of staying in front of their rush and limiting their chances," Capitals forward Tom Wilson said. "They got some good looks and they made it count. Not a great way to finish but it is what it is."