Green allowed one run over two innings and struck out two in Wednesday's loss to Toronto.
The 26-year-old entered in the sixth with starter Michael Pineda lasting only three innings. Green gave up a solo home run to Russell Martin in the seventh, which tied the game 6-6. The right-hander has a 2.03 ERA and 0.77 WHIP with 38 strikeouts across 31 innings this season, and has proven to be a valuable long reliever out of the Yankees' bullpen.