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.
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend
Pot vending machine to debut