Carolina extended its home winning streak to eight games, the Hurricanes' longest home streak since their Stanley Cup championship season in 2005-06. Carolina beat the Southeast Division-leading Capitals for the third time this season.
"The fans have created a tremendous atmosphere here, and we've been able to rally behind them," Ward said.
"You've got to play those guys tough," Corvo said. "You've got to get under their skin. We took a lot of their weapons away."
Brind'Amour opened the scoring at 3:53 of the second period, beating Jose Theodore with a low shot from the slot. Brind'Amour has goals in five of his past eight games.
"Scoring the first goal has been key," Ward said. "Despite the start we had, we were able to get the lead and go from there."
Green tied it with 33 seconds left in the second period when he collected a lively rebound in the center of the right circle and beat Ward, who was unable to get back across the crease to defend Green's quick release.
But that was the only offense the Capitals were able generate. Washington coach Bruce Boudreau said his team's effort was not the same in the third period.
"We were really good in the first, and then we started to turn the puck over in the second and third," Boudreau said. "We made a couple of mistakes."
The Hurricanes got the winner from Pitkanen 4:42 into the third period just after killing off Brind'Amour's hooking penalty. Pitkanen took a pass from Eric Staal as he skated in front of the crease and flipped it in with a backhand.
Babchuk scored with 6:17 left after taking a pass from Dennis Seidenberg at the top of the crease. Babchuk's first shot was blocked, but he scored on the rebound.
"The puck went into our net too many times," Washington forward Sergei Fedorov said. "We were just disorganized."
Corvo's goal came in the final minute when he cleared the puck on a penalty kill. Washington pulled Theodore for an extra skater, and the net was open.
Carolina has been in a tight race for the remaining playoff spots in the Eastern Conference and will play all but two of its remaining seven games on home ice.
Other games: : Joe Pavelski had a goal and two assists, Joe Thornton added another timely goal, and the host Sharks won back-to-back games for just the second time in nearly four weeks, beating the Stars, 5-2. Evgeni Nabokov made 23 saves, Devin Setoguchi had a goal and an assist, Milan Michalek also scored and captain Patrick Marleau added an empty-netter to help the Sharks pull within a point of the Red Wings for the NHL lead. ... Ex-Buffalo captain Chris Drury scored during host New York's three-goal second period that carried the Rangers past the Sabres, 5-3.