Alex Ovechkin added two assists for Southeast Division-leading Washington, which improved to 7-0-1 in its last eight meetings with Carolina.
Anthony Stewart scored on a deflection and Cam Ward stopped 27 shots for the Hurricanes. They have lost five of seven but did not earn a point for just the third time in that span.
The Capitals have won two straight since a two-game slide on the road interrupted their club-record 7-0 start. They entered averaging a league-best 3.9 goals, and showed plenty of firepower early in the second period by scoring two goals in a little more than a minute.
Halpern — a healthy scratch for Tuesday night's overtime win over Anaheim — tied it at 1 when he charged down the middle and laid out while sending the puck past Ward with 18:32 left. Not long after that, Washington took the lead when Marcus Johansson scooped up the puck at the blue line and fed it to Brouwer for a tap-in with 17:23 remaining to make it 2-1.
Carlson's slap shot from behind the circle made it 3-1 with 16:45 left in the third, Eakin extended the lead to three midway through the third with his first career goal and Backstrom added a goal with 4:08 left.
That was more than enough offense to support Neuvirth. The backup to Tomas Vokoun made just his third appearance of the season and stopped the last 20 shots he faced over the final 56½ minutes.
The only player to put the puck past him was Stewart, who gave the Hurricanes a 1-0 lead roughly 3½ minutes in with his deflected goal. After Carolina won a draw, the puck made its way to Jay Harrison inside the blue line, and he unloaded a shot that clipped Stewart's stick on its way into the net.
Jeff Skinner thought he scored on a power play midway through the second when he stuffed a shot past Neuvirth, but an official blew the whistle before the puck got by the goalie, prompting the Hurricanes' second-year star to slam his stick on the ice in frustration.
NOTES: Brouwer added an assist on the Capitals' fifth goal. ... Ovechkin has five points in three games. ... C Mathieu Perreault was a healthy scratch for Washington. ... The Hurricanes haven't beaten the Capitals in regulation at home since 2009.