Washington has 54 points, one more than New Jersey, Pittsburgh, Chicago and San Jose. Washington won its third straight and ended New Jersey's five-game winning streak.
The Capitals lost their first three games against the Devils despite taking first-period leads in each. Washington took a 2-0 lead in this game and never let up.
"I think we played a complete game," said Washington coach Bruce Boudreau. "I thought it was a great effort on our part."
Brodeur had a 36-12-4 record with a 2.11 goals-against average versus Washington heading into the game. But the offensive pressure and Neuvirth's strong effort gave the Capitals their first win against New Jersey this season.
"These guys had 40 shots on net," Brodeur said. "They're explosive offensively. When you give that kind of a team that many good scoring chances, with that talent, they'll put the puck in the net."
But the 21-year old goalie -- playing in just his 10th NHL game -- couldn't hide his delight at beating Brodeur.
"I'm feeling unbelievable right now," Neuvirth said. "I just beat the best goalie in the world, so it's amazing. I used to watch him on TV, so it was something special."
Washington's top line of Ovechkin, Backstrom and Alexander Semin -- who signed a one-year contract extension Saturday -- also was special. They combined for two goals, five assists and 14 shots and finished plus-3.
It was Ovechkin's third consecutive three-point night.
"We understand each other a lot, and you can see how we control the puck in the offensive zone and we feel pretty good and nobody can stop us," Ovechkin said. "We have to continue playing."
Washington center Dave Steckel also played well. He got an assist and won 15 of 21 face-offs, including all eight of his first-period draws, helping the Capitals maintain possession and keep pressure on the Devils.
Ovechkin opened the scoring at 4:09 of the first period. Backstrom won the draw and sent it back to Ovechkin, who scored from the left circle.
The Capitals made it 2-0 on a fluke goal with 6:06 left in the first period. Matt Bradley fired a shot that New Jersey's Mike Mottau appeared to deflect, and the puck was sailing over the net when Brodeur reached high for it. But the puck hit his glove, dropped to the ice and rolled in.
The Devils scored later in the period on Pelley's goal. They appeared to tie it early in the second period, but Jay Pandolfo's goal was waved off.
Backstrom gave the Capitals a 3-1 lead when he scored from in front with 10:08 left in the period. Semin and Ovechkin assisted on that goal. Ovechkin and Backstrom both earned assists on Mike Green's third-period goal that made it 4-1.
Backstrom's first-period assist was his 200th NHL point -- in just 202 games. ... The Capitals lead the league with 49 first-period goals. ... The Devils lost for only the third time on the road this season.