Granderson finished off a four-run seventh inning with a two-run double and then added a solo homer in the ninth, his 20th of the season.
The Yankees gave Manager Joe Girardi his 500th career victory while halting Washington's six-game winning streak, its longest of the year.
Alex Rodriguez also singled in a run in the third, giving him 1,924 RBI for his career. That ties him with Jimmy Foxx for the sixth most in major league history.
Hughes (7-5) allowed a run on six hits over six innings. He is 4-0 over his last five starts.
Gio Gonzalez (8-3) suffered the loss, giving up three runs on five hits in six-plus innings.