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.
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