Neuvirth appeared in his 31st NHL game spread over three seasons.
He was protecting a 1-0 lead heading into the third period, but Nicklas Backstrom scored twice in the final stanza to help boost Washington to its sixth win in eight games.
Backstrom gave the Capitals a 2-0 lead 7:37 into the third and added a shorthanded goal into an empty net with 1:28 to go.
The first Washington goal came from Matt Hendricks midway through the first period.
It was Carolina's home opener after the Hurricanes had played their first seven on the road. They went 4-3 on the extended journey.
Cam Ward allowed two goals on 30 shots.