Svechnikov put the Hurricanes ahead 3-2 with a third-period power-play goal at 13:56. He took a pass out of the corner from Nikolaj Ehlers, drew Washington goalie Logan Thompson across the crease and lifted a backhand near the top of the crease.
Svechnikov earned an assist on an empty-net goal at 18:33, setting up Mark Jankowski, who extended his scoring streak to five games.
Eric Robinson scored and Pyotr Kochetkov made 20 saves for the Hurricanes (6-1-1).
Hurricanes forward Taylor Hall left the game in the second period with an upper-body injury and did not return.
Boone Jenner and Justin Holl scored, and Thompson made 31 saves for the Capitals (3-3-0), who have lost two in a row.
Jenner gave Washington a 1-0 lead at 9:26 of the first period. Sean Walker blocked Ryan Leonard’s shot, but the Capitals forward got his own rebound and passed to Jenner, who beat Kochetkov with a short-side wrist shot.
The Hurricanes tied it 1-1 at 3:58 of the second period. Thompson fended off two shots by William Carrier, but Svechnikov poked the puck in the net from under Thompson’s left pad.
Holl put the Capitals ahead 2-1 at 6:39 when he scored through a screen from the top of the right face-off circle. It was the veteran defenseman's Washington debut after he was recalled from Hershey of the American Hockey League on Monday.
Carolina tied it 2-2 at 18:49 when Eric Robinson’s shot deflected off the stick of Washington defenseman Martin Fehervary and into the net.