Sourdif knocked in a loose puck at the right post to help the Capital win their second straight game for the first time since a six-game streak Nov. 24-Dec. 3.
Jakob Chychrun had a goal and an assist for the Capitals (27-22-7). Aliaksei Protas had two assists, and Clay Stevenson made 19 saves for his first NHL win in his second game.
Mark Jankowksi, Sebastian Aho and Shayne Gostisbehere scored for the Hurricanes (33-15-6), who have a seven-game point streak (5-0-2) and are 9-1-3 in their past 13. Frederik Andersen made 38 saves.
Chychrun tied it 3-3 at 13:18 of the third period, scoring on a stick-side wrist shot from the high slot off a pass from Protas.
Jankowski gave the Hurricanes a 1-0 lead at 13:27 of the first period. William Carrier gloved down the puck and passed to Jankowski, who scored on a snap shot from in front.
Aho made it 2-0 at 17:51. Capitals defenseman John Carlson fanned on a pass attempt above the left circle and Aho got the puck, skated into the slot and put a snap shot past Stevenson.
Gostisbehere pushed it to 3-0 at 4:16 of the second period when he scored over Stevenson’s right shoulder with a wrist shot from along the wall.
Hendrix Lapierre cut the deficit to 3-1 at 7:52, putting in his own rebound in front when Andersen was unable to control the puck.
Dylan Strome pulled the Capitals within 3-2 at 14:58 when he tipped in a centering pass from Protas.