Faking a shot to freeze Buffalo Sabres goalie Jhonas Enroth, Ovechkin fed a pass through the middle to a wide-open Green, who snapped it into the open right side one minute into overtime and sealed Washington's 5-4 win on Tuesday night.
"Oh, he screamed so loud, but I knew he was out there," said Ovechkin, who finished with two goals and two assists. "I gave him the pass. It was a little bit forward but it was good for him. It was good for our team. He reached it and put it in."
The setup was also payback for a goal Ovechkin was credited with in putting the Capitals up 2-0 early the first period. That's when Green's shot banked in off Ovechkin's leg and into the net.
"Yeah, I felt sorry for Greeny," Ovechkin said. "But it is what it is."
Green was grateful to be able to finish off a game in which the Capitals never trailed.
"He made a great play," Green said. "I know it's tough for him not to shoot the puck, but what an unselfish play that was."
Green had two goals and an assist, and Troy Brouwer added a goal and assist. Washington (24-21-8) was coming off a 5-0 win at Montreal on Saturday and won consecutive games for the first time since Jan. 9-10.
The Capitals have suddenly rediscovered their offense. They've combined for 10 goals in two games after managing just eight during an 0-5-2 skid. Washington's power play also came to life in converting two of three chances after going 1 for 32 in its previous nine games.
Enroth stopped 30 shots to drop to 1-11-4 on the season and extend his losing streaking to 12 straight (0-9-3)
Hodgson focused on the positives by noting how the Sabres refused to fold in rallying back each time the Capitals went ahead.
"I think we had a lot of character in that room," said Hodgson, who has six goals and 10 points in eight games since returning from a thumb injury. "We showed a lot of guts battling back."
Hodgson forced overtime by scoring on a solid individual play 6:48 into the third period.
With a delayed penalty being called against Washington forward Jason Chimera, Hodgson got to a loose puck in the right circle. He then weaved his way past two defenders and lifted a backhander over goalie Braden Holtby's right shoulder.
Despite playing on back-to-back nights following a 3-0 loss at Pittsburgh, the Sabres found their stride as the game progressed. They outshot Washington 10-1 through the first 10 minutes of the third period and 13-6 over the final 21 minutes.
What the Sabres couldn't overcome was Ovechkin, who showed no signs of the lower body injury that sidelined him for two games last week. With a goal and assist against Montreal, the Capitals' captain now has six points in his past two, and combined for eight goals and six assists in his past 11.
Ovechkin upped his NHL-leading goal total to 38 and enjoyed his 14th multipoint game of the season. He also upped his career total to 790 points, moving into second on the Capitals' list, one ahead of Mike Gartner.
"He's the face of the franchise. And we count on him every night," Capitals coach Adam Oates said, noting the distractions Ovechkin faces in preparing to represent Russia at the Sochi Winter Games in two weeks. "He's had a lot of demands on his time being pulled in a lot of different directions. Glad to see him rewarded tonight. We needed the points, and he got it done for us."
Capitals forward Nicklas Backstrom was shaken up after being elbowed to the head by Sabres defensman Mike Weber in front of the benches with a minute left in the third period. Backstrom was skating toward the bench well away from the play when Weber reached up and struck him.
Weber was not penalized and could potentially be disciplined by the NHL.
Sabres RW Drew Stafford missed his second game with an upper body injury. ... Capitals C Ryan Stoa was a healthy scratch after being called up from AHL Hershey earlier in the day. Stoa appeared in his first NHL game since playing 25 during the 2010-11 season with Colorado. ... Earlier in the day, NHL Commissioner Gary Bettman revealed to The Associated Press that the league is considering the Sabres' proposal to relocate the annual pre-draft combine from Toronto to Buffalo, where the team is building a two-rink hockey/entertainment complex.