Green scored with 3:44 left in overtime, giving Washington a harrowing 4-3 win over the Hurricanes on Friday.
Alexander Semin had two goals for the Capitals, who took their first lead on a goal by Tomas Fleischmann with 17:08 left in regulation. But Green later forked over the puck with Washington on the power play, and Carolina's Tim Gleason turned the miscue into a breakaway goal with 6:30 to go.
"I didn't even see him behind the guy that was standing in front of me," Green said. "I was chasing him, but he had a great shot."
In overtime, however, Green slammed home a wrist shot from between the circles off a pass from Nicklas Backstrom.
"I got lucky there and was just excited it went in," Green said. "I didn't have a great game, so it's a great feeling."
The Capitals entered with the best record in the NHL and Carolina had the worst. But the Hurricanes converted two of their first three shots to take a 2-0 lead with 14 minutes elapsed.
Semin tied it by scoring twice in the second period, setting the stage for the dramatic third period.
Then came Green's goal in overtime. Despite scoring the game-winner, the standout defenseman apologized for his play afterward.
"I said, 'No need to apologize,"' Capitals coach Bruce Boudreau said. "Really good players, if they're having a bad game, still have a tendency to step up and be in the limelight at some point on a positive note."
Gleason had his face bloodied by a puck but stayed on the ice. He received 30 stitches afterward.
"That shows the type of player he is, the character he has, the toughness he brings to the team," teammate Eric Staal said. "It was a huge goal he had. It got us a point."
"We battled back to get that point," Staal said. "For us, right now, one point doesn't do much. It was tough to lose in overtime."
In rebounding from a 3-0 loss at Buffalo on Wednesday night, the Capitals outshot Carolina 37-16 during regulation and improved to 8-0-0 this season within the Southeast Division.
Tlusty put the Hurricanes up 1-0 at 2:01 of the first period with his first goal since March 29, 2008, with Toronto. Tlusty was making his Carolina debut after being called up from Albany of the AHL earlier Friday.
"We're playing at home in front of our fans and we were two goals down. There was nothing else to do but start playing great and start shooting," Semin said through an interpreter. "Otherwise we wouldn't have won that game."
After outshooting Carolina 14-4 in the first period, the Capitals needed more than 7½ minutes to get their first shot on goal in the second period.
Semin cut the gap to 2-1 with a shot from the right circle that went through Brett Carson's legs and over Ward's shoulder.
"Up until that point we couldn't score," Semin said. "Once we scored, we started playing great."
Carolina missed a chance to restore its two-goal cushion late in the second period when it was determined by a replay that Tuomo Ruutu kicked the puck into the net with the Hurricanes on the power play.
Semin tied it with less than a second remaining, lifting a loose puck over the prone Ward.
- Besides calling up Tlusty and Dwyer, Carolina placed forwards Erik Cole and Chad LaRose on injured reserve.
- Before Friday, the Capitals had outscored the opposition 39-15 in the first period.
- Washington RW Mike Knuble returned after missing 12 games because of a broken finger.