Ovechkin also had two goals and added a pair of assists for the Capitals, who logged a second consecutive win on the heels of a seven-game skid.
Green assisted on one of Ovechkin's goals and Troy Brouwer helped out with a goal and an assist.
Braden Holtby turned aside 23-of-27 shots.
Cody Hodgson scored twice for Buffalo, losers of seven in eight.
Philip Varone and Christian Ehrhoff also scored.
Jhonas Enroth stopped 30 shots for the Sabres.
2014 amfAR Inspiration Gala [PHOTOS]
Julius Randle breaks leg during NBA debut